According to the U.S. Tax Court, Antarctica is not a foreign country.
Why does this matter? The general rule is that Americans must pay taxes on their worldwide income under Internal Revenue Code Section 61, but, "the amount received by such individual from sources within a foreign country or countries which constitute earned income attributable to services performed by such individual" is tax fee, under Internal Revenue Code Section 911, subject to certain limitations.
Why? An international treaty states that Antarctica is a sovereignless region. According to the Tax Court, this means it isn't a foreign country for tax purposes, even though the U.S. Supreme Court has ruled in non-tax cases that Antarctica is a foreign country.
This isn't necessarily a horrible ruling. The Section 911 tax exemption was based on the idea that you would be paying taxes where you live, which Americans in Antarctica do not (then again, governmental services in Antarctica aren't so hot either, so maybe it is a fair deal). This will also probably be a relevant precedent NASA sends astronauts to the Moon again, or to Mars, and they try to escape paying taxes while working there. (One also wonders if a reporter working in Guantanamo Bay, Cuba has to pay taxes on the income he earns while working there.)
The Moral of the story: If you want to avoid paying U.S. income taxes on your earned income, go someplace nice, like the Caymans.
The case is: Dave Arnett v. Commissioner, 126 TC No. 5, Dkt. No. 8866-03, 1/25/2006.
Hat tip to tax publisher RIA.