Q:

Did the U.S. sign a treaty with another government about the legality of a single coin?

On the Wikipedia page about the golden $20 double eagle coin, there is the following sentence:

This piece is unique as the only 1933 double eagle the U.S. government has deemed legal for its citizens to own (having been negotiated as such through terms of a U.S. treaty with a foreign government).

It seems very weird to me that another, foreign government would interfere with the legality of a single coin. Furthermore, the statement is so vague (which government?), that I doubt it. 
Did the U.S. sign a treaty with another government about the legality of a single coin?

A:

I believe the specific coin the article is referring to is the Egyptian Gold Double Eagle.
I believe the treaty your article refers to might possibly be one we had with Egypt during the 1940's (although I couldn't say which one).  It's poorly written as it is on Wikipedia however, which is probably why there is a [citation needed] tag next to it.
When FDR issued Executive Order 6102 banning private ownership of gold in 1933, the gold Double Eagle coins of that year had already been minted, but not circulated yet.  All but two of the uncirculated coins were ordered destroyed (the two exemptions were to be sent to the Smithsonian Institute where they remain today), but at least 20 of those coins are now known to have been stolen from the Mint.  Because they were never circulated, they remain the property of the U.S. government and being in possession of stolen property is illegal pretty much everywhere.
In 1944, one of the stolen coins wound up in the hands of King Farouk of Egypt, who had purchased it at an auction.  Neither he nor the Treasury Department knew at the time that the coins had been stolen.  King Farouk applied in good faith for an export license as per U.S. law.  This might be where a treaty provision would apply if there were a treaty covering this.  In either case, the Treasury granted the license before they fully understood what he had.  The license was granted in error.
The government tried to get the coin back, but WWII was being fought in northern Africa at the time and things were a bit chaotic.  Then in 1952, King Farouk was deposed by a coup d'etat and much of his rare antiquities collection was lost, including the coin.
In 1996, a 1933 gold Double Eagle surfaced at a New York auction by a British coin dealer.  He was arrested by the Secret Service and the coin was seized.  The dealer claimed that it was the Egyptian coin he had, and that it was legally exported to King Farouk.  The Treasury Department could not prove his story one way or the other (since every coin is identical), so the charges against him were dropped.  But the Secret Service kept the coin and the dealer sued the U.S. government to get it back.
A settlement was reached in 2001 where the two parties agreed that the coin was U.S. property but would be monetized (making it officially legal tender) so it could be sold at auction.  The proceeds were to be split between the Treasury and the coin dealer.  Within minutes, the coin was sold for $7.5 million USD to an anonymous buyer -- the highest price ever paid for a rare coin.
So the lesson here is that there was no "interference" by any foreign government regarding the legality of the coin, and no treaty arrangement that makes it legal today.  The fact that this one and only specimen is legal tender results from a settlement reached by a U.S. court.  It (and only it) is therefore legal to own, and should it surface in some other country (hopefully with authentication documents intact), that country is under no obligation to seize it or arrest the person who has it.

