For nearly a hundred years absinthe has been regarded as "banned in the United States", although this is not completely true or accurate.

There is no law which prohibits absinthe by name, and no law which prohibits absinthium wormwood in beverages, but any beverage which contains in excess of 10ppm of thujone is prohibited from being imported into, or produced for sale and consumption in, the United States.

For nearly a hundred years absinthe has been regarded as "banned in the United States", although this is not completely true or accurate.

There is no law which prohibits absinthe by name, and no law which prohibits absinthium wormwood in beverages, but any beverage which contains in excess of 10ppm of thujone is prohibited from being imported into, or produced for sale and consumption in, the United States.

NOTE: No regulations have changed.  Prior to May 2007 it was not widely known that the official threshold for thujone analysis—10ppm—is such that it permits, or effectively "legalizes", many European absinthes.

Several authentic absinthes are now available for purchase at liquor stores and bars in the US.  This is a major breakthrough, as many brands will follow.

Accordingly, the absinthe referred to in the below statutes would be absinthe which is non-compliant with the current limits or is illegally introduced to the country.

Most of the laws which impact absinthe in the US are out-dated, unfair, convoluted, illogical, self-contradictory, un-evenly enforced and misunderstood even by those responsible enforcing them. In short, it's a collection of bad law.

These laws and rules are presented here in an effort to aid our readers in making well-informed and wise decisions, as well as to help illustrate the complex legalities involving absinthe.

IMPORTATION

US Customs and Border Protection enforces the laws set by other agencies, i.e the FDA, USDA, TTB, etc.  All emphasis added.

From US Customs Web Site:

Know Before You Go - Tips for Visitors to the United States

Prohibited and Restricted Items
• Absinthe (Alcohol)
• Automobiles
• Biologicals
• Ceramic Tableware
• Cultural Artifacts and Cultural Property (Art/Artifacts)
• Dog and Cat Fur
• Drug Paraphernalia
• Firearms
• Fish and Wildlife
• Food Products (Prepared)
• Fruits and Vegetables
• Game and Hunting Trophies
• Gold
• Meats, Livestock, and Poultry
• Medication
• Merchandise from Embargoed Countries
• Pets
• Plants and Seeds
• Soil
• Textiles and Clothing
• Trademarked and Copyrighted Articles

CBP (Customs and Border Protection) has been entrusted with enforcing some 400 laws for 40 other government agencies, such as the U.S. Fish and Wildlife Service and the U.S. Department of Agriculture. These other agencies have a need to know what people bring into the United States, but they are not always at ports of entry, guarding our borders. CBP officers are always at ports of entry—their primary mission is to safeguard America's borders.

The products we need to prevent from entering the United States are those that would injure community health, public safety, American workers, children, or domestic plant and animal life, or those that would defeat our national political interests. Sometimes the products that cause injury, or have the potential to do so, may seem fairly innocent. But, as you will see from the material that follows, appearances can be deceiving.

Before you leave for your trip abroad, you might want to talk to CBP about the items you plan to bring back to be sure they're not prohibited or restricted. Prohibited means the item is forbidden by law to enter the United States. Examples of prohibited items are dangerous toys, cars that don't protect their occupants in a crash, or illegal substances like absinthe* and Rohypnol. Restricted means that special licenses or permits are required from a federal agency before the item is allowed to enter the United States. Examples of restricted items include firearms and certain fruits, vegetables, pets, and textiles.

 *This passage shows that even the copy writers for the CBP are unaware that absinthe is not an illegal or controlled "substance."

***

Absinthe (Alcohol)
The importation of Absinthe and any other liquors or liqueurs that contain Artemisia absinthium is prohibited.

[ed. note: They do not say which law prohibits it, as in fact there are none.  Artemisia absinthium is on the list of FDA-approved ingredients.]

***

Top 10 Tips

6)    Know the difference between prohibited merchandise (such as ivory, tortoise shell products, absinthe, and counterfeit items) and restricted merchandise.

United States Code

TITLE 19 - CHAPTER 4 - SUBTITLE III - Part V - Sec. 1595.
Sec. 1595. - Searches and seizures
(a) Warrant
     (1)  If any officer or person authorized to make searches and seizures has probable cause to believe that -
         (A)  any merchandise upon which the duties have not been paid, or which has been otherwise brought into the United States unlawfully;
         (B)  any property which is subject to forfeiture under any provision of law enforced or administered by the United States Customs Service; or
         (C)  any document, container, wrapping, or other article which is evidence of a violation of section 1592 of this title involving fraud or of any other law enforced or administered by the United States Customs Service,

is in any dwelling house, store, or other building or place, he may make application, under oath, to any justice of the peace, to any municipal, county, State, or Federal judge, or to any Federal magistrate judge, and shall thereupon be entitled to a warrant to enter such dwelling house in the daytime only, or such store or other place at night or by day, and to search for and seize such merchandise or other article described in the warrant.

***

TITLE 19 - CHAPTER 4 - SUBTITLE III - Part V - Sec. 1595a.

(a) Importation , removal, etc. contrary to laws of United States
Except as specified in subsection (b) or (c) of section 1594 of this title, every vessel, vehicle, animal, aircraft, or other thing used in, to aid in, or to facilitate, by obtaining information or in any other way, the importation , bringing in, unlading, landing, removal, concealing, harboring, or subsequent transportation of any article which is being or has been introduced, or attempted to be introduced, into the United States contrary to law, whether upon such vessel, vehicle, animal, aircraft, or other thing or otherwise, may be seized and forfeited together with its tackle, apparel, furniture, harness, or equipment.

(b) Forfeitures and other penalties
Penalty for aiding unlawful importation
Every person who directs, assists financially or otherwise, or is in any way concerned in any unlawful activity mentioned in the preceding subsection shall be liable to a penalty equal to the value of the article or articles introduced or attempted to be introduced.

[</b>United States Postal Service<b>] United States Postal Service
Domestic Mail Manual

C024 Other Restricted or Nonmailable Matter

7.0 Intoxicating Liquor:
A potable beverage is nonmailable if it is of 0.5% or more alcoholic content by weight, which is taxable under Chapter 51, Internal Revenue Service Code. The product may be mailed if it conforms to applicable requirements of the Internal Revenue Service and Food and Drug Administration and is not an alcoholic beverage, poisonous, or flammable.

 
[Manufacture] MANUFACTURE

Where the FDA regulates thujone levels:

[Code of Federal Regulations]
[Title 21, Volume 3]
[Revised as of April 1, 2004]
[CITE: 21CFR172.510]

TITLE 21--FOOD AND DRUGS
CHAPTER I--FOOD AND DRUG ADMINISTRATION
DEPARTMENT OF HEALTH AND HUMAN SERVICES
SUBCHAPTER B - FOOD FOR HUMAN CONSUMPTION (CONTINUED)
PART 172 -- FOOD ADDITIVES PERMITTED FOR DIRECT ADDITION TO FOOD FOR HUMAN CONSUMPTION
Subpart F -- Flavoring Agents and Related Substances
Sec. 172.510 Natural flavoring substances and natural substances used in conjunction with flavors.

Relevant Excerpt:

Artemisia (wormwood), Artemisia spp, Finished food thujone free...
As determined by using the method (or, in other than alcoholic beverages, a suitable adaptation thereof) insection 9.129 of the "Official Methods of Analysis of the Association of Official Analytical Chemists," 13thEd. (1980).

Note that as this is written it applies to all Artemisia species, not just absinthium.  The AOAC Method can be found here .
 

From the TTB Website FAQ:

(emphasis added)
Spirits

You cannot produce spirits for beverage purposes without paying taxes and without prior approval of paperwork to operate a distilled spirits plant.  [See 26 U.S.C. 5601 & 5602 for some of the criminal penalties.]  There are numerous requirements that must be met that make it impractical to produce spirits for personal or beverage use.  Some of these requirements are paying special tax, filing an extensive application, filing a bond, providing adequate equipment to measure spirits, providing suitable tanks and pipelines, providing a separate building (other than a dwelling) and maintaining detailed records, and filing reports.  All of these requirements are listed in 27 CFR Part 19.

I've seen ads for home distilling equipment in catalogs ("turn wine into brandy," "make your own essential oils"). Is it legal to buy and use a still like that?
Under Federal rules administered by TTB, it depends on how you use the still. You may not produce alcohol with these stills unless you qualify as a distilled spirits plant (see earlier question). However, owning a small still and using it for other purposes is allowed. You should also check with your State and local authorities - their rules may differ.

A still is defined as apparatus capable of being used to separate ethyl alcohol from a mixture that contains alcohol. Small stills (with a cubic distilling capacity of a gallon or less) that are used for laboratory purposes or for distilling water or other non-alcoholic materials are exempt from our rules.

If you buy a small still and use it to distill water or extract essential oils by steam or water extraction methods, you are not subject to TTB requirements. If you produce essential oils by a solvent method and you get alcohol as a by-product of your process, we consider that distilling. Even though you are using and recovering purchased alcohol, you are separating the alcohol from a mixture - distilling.

 
[United States Code on Unregulated Distilling] United States Code on Unregulated Distilling

TITLE 26  - Subtitle E - CHAPTER 51 - Subchapter J - PART I - Sec. 5601 - 5602

Sec. 5601. - Criminal penalties

Any person who -

(1) Unregistered stills

has in his possession or custody, or under his control, any still or distilling apparatus set up which is not registered, as required by section 5179(a); or

(2) Failure to file application

engages in the business of a distiller or processor without having filed application for and received notice of registration, as required by section 5171(c); or

(3) False or fraudulent application

engages, or intends to engage, in the business of distiller, warehouseman, or processor of distilled spirits, and files a false or fraudulent application under section 5171; or

(4) Failure or refusal of distiller, warehouseman, or processor to give bond

carries on the business of a distiller, warehouseman, or processor without having given bond as required by law; or

(5) False, forged, or fraudulent bond

engages, or intends to engage, in the business of distiller, warehouseman, or processor of distilled spirits, and gives any false, forged, or fraudulent bond, under subchapter B; or

(6) Distilling on prohibited premises

uses, or possesses with intent to use, any still, boiler, or other utensil for the purpose of producing distilled spirits, or aids or assists therein, or causes or procures the same to be done, in any dwelling house, or in any shed, yard, or inclosure connected with such dwelling house (except as authorized under section 5178(a)(1)(C)), or on board any vessel or boat, or on any premises where beer or wine is made or produced, or where liquors of any description are retailed, or on premises where any other business is carried on (except when authorized under section 5178(b)); or

(7) Unlawful production, removal, or use of material fit for production of distilled spirits

except as otherwise provided in this chapter, makes or ferments mash, wort, or wash, fit for distillation or for the production of distilled spirits, in any building or on any premises other than the designated premises of a distilled spirits plant lawfully qualified to produce distilled spirits, or removes, without authorization by the Secretary, any mash, wort, or wash, so made or fermented, from the designated premises of such lawfully qualified plant before being distilled; or

(8) Unlawful production of distilled spirits

not being a distiller authorized by law to produce distilled spirits, produces distilled spirits by distillation or any other process from any mash, wort, wash, or other material; or

(9) Unauthorized use of distilled spirits in manufacturing processes

except as otherwise provided in this chapter, uses distilled spirits in any process of manufacture unless such spirits -

(A) have been produced in the United States by a distiller authorized by law to produce distilled spirits and withdrawn in compliance with law; or

(B) have been imported (or otherwise brought into the United States) and withdrawn in compliance with law; or

(10) Unlawful processing

engages in or carries on the business of a processor -

(A) with intent to defraud the United States of any tax on the distilled spirits processed by him; or

(B) with intent to aid, abet, or assist any person or persons in defrauding the United States of the tax on any distilled spirits; or

(11) Unlawful purchase, receipt, or processing of distilled spirits

purchases, receives, or processes any distilled spirits, knowing or having reasonable grounds to believe that any tax due on such spirits has not been paid or determined as required by law; or

(12) Unlawful removal or concealment of distilled spirits

removes, other than as authorized by law, any distilled spirits on which the tax has not been paid or determined, from the place of manufacture or storage, or from any instrument of transportation, or conceals spirits so removed; or

(13) Creation of fictitious proof

adds, or causes to be added, any ingredient or substance (other than ingredients or substances authorized by law to be added) to any distilled spirits before the tax is paid thereon, or determined as provided by law, for the purpose of creating fictitious proof; or

(14) Distilling after notice of suspension

after the time fixed in the notice given under section 5221(a) to suspend operations as a distiller, carries on the business of a distiller on the premises covered by the notice of suspension, or has mash, wort, or beer on such premises, or on any premises connected therewith, or has in his possession or under his control any mash, wort, or beer, with intent to distill the same on such premises; or

(15) Unauthorized withdrawal, use, sale, or distribution of distilled spirits for fuel use

Withdraws, [1] uses, sells, or otherwise disposes of distilled spirits produced under section 5181 for other than fuel use; shall be fined not more than $10,000, or imprisoned not more than 5 years, or both, for each such offense.

(b) Presumptions

Whenever on trial for violation of subsection (a)(4) the defendant is shown to have been at the site or place where, and at the time when, the business of a distiller or processor was so engaged in or carried on, such presence of the defendant shall be deemed sufficient evidence to authorize conviction, unless the defendant explains such presence to the satisfaction of the jury (or of the court when tried without jury)

Sec. 5602. - Penalty for tax fraud by distiller
Whenever any person engaged in or carrying on the business of a distiller defrauds, attempts to defraud, or engages in such business with intent to defraud the United States of the tax on the spirits distilled by him, or of any part thereof, he shall be fined not more than $10,000, or imprisoned not more than 5 years, or both. No discontinuance or nolle prosequi of any prosecution under this section shall be allowed without the permission in writing of the Attorney General.

  [Revised Code of the State of Washington] From the Revised Code of the State of Washington

Since the Wormwood Society is based in Seattle, Washington we felt it appropriate to include relevant state laws.  Most states have similar laws, varying in the degree of severity but having the same aim: avoiding disruption of state revenues from alcohol sales.

Title 66 - ALCOHOLIC BEVERAGE CONTROL

RCW 66.12.010 - Wine or beer manufactured for home use.
Nothing in this title other than RCW 66.28.140 [re: transport of family wine or beer to tastings and judging], applies to wine or beer manufactured in any home for consumption therein, and not for sale.

RCW 66.24.140  - Distiller's license -- Fee.
There shall be a license to distillers, including blending, rectifying and bottling; fee two thousand dollars per annum: PROVIDED, That the board shall license stills used and to be used solely and only by a commercial chemist for laboratory purposes, and not for the manufacture of liquor for sale, at a fee of twenty dollars per annum: PROVIDED, FURTHER, That the board shall license stills used and to be used solely and only for laboratory purposes in any school, college or educational institution in the state, without fee: PROVIDED, FURTHER, That the board shall license stills which shall have been duly licensed as fruit and/or wine distilleries by the federal government, used and to be used solely as fruit and/or wine distilleries in the production of fruit brandy and wine spirits, at a fee of two hundred dollars per annum.

RCW 66.32.010 - Possession of contraband liquor.
Except as permitted by the board, no liquor shall be kept or had by any person within this state unless the package in which the liquor was contained had, while containing that liquor, been sealed with the official seal adopted by the board, except in the case of:
     (1) Liquor imported by the board; or
     (2) Liquor manufactured in the state for sale to the board or for export; or
     (3) Beer, purchased in accordance with the provisions of law; or
     (4) Wine or beer exempted in RCW 66.12.010.

RCW 66.32.020  - Search warrant -- Search and seizure.
If, upon the sworn complaint of any person, it is made to appear to any judge of the superior court or district court, that there is probable cause to believe that intoxicating liquor is being manufactured, sold, bartered, exchanged, given away, furnished, or otherwise disposed of or kept in violation of the provisions of this title, such judge shall, with or without the approval of the prosecuting attorney, issue a warrant directed to a civil officer of the state duly authorized to enforce or assist in enforcing any law thereof, or to an inspector of the board, commanding the civil officer or inspector to search the premises, room, house, building, boat, vehicle, structure or place designated and described in the complaint and warrant, and to seize all intoxicating liquor there found, together with the vessels in which it is contained, and all implements, furniture, and fixtures used or kept for the illegal manufacture, sale, barter, exchange, giving away, furnishing, or otherwise disposing of the liquor, and to safely keep the same, and to make a return of the warrant within ten days, showing all acts and things done thereunder, with a particular statement of all articles seized and the name of the person or persons in whose possession they were found, if any, and if no person is found in the possession of the articles, the return shall so state.

RCW 66.44.140 - Unlawful sale, transportation of spirituous liquor without stamp or seal -- Unlawful operation, possession of still or mash.
Every person who shall sell or offer for sale, or transport in any manner, any spirituous liquor, without government stamp or seal attached thereto, or who shall operate without a license, any still or other device for the production of spirituous liquor, or shall have in his possession or under his control any mash capable of being distilled into spirituous liquor except as provided in RCW 66.12.130 , shall be guilty of a gross misdemeanor and upon conviction thereof shall upon his first conviction be fined not less than five hundred dollars and confined in the county jail not less than six months, and upon second and subsequent conviction shall be fined not less than one thousand dollars and confined in the county jail not less than one year.

RCW 66.44.160 - Illegal possession, transportation of alcoholic beverages.
Except as otherwise provided in this title, any person who has or keeps or transports alcoholic beverages other than those purchased from the board, a state liquor store, or some person authorized by the board to sell them, shall be guilty of a violation of this title.