Here's another link about dual citizenship requirements for the US. This issue got national attention in Canada when a Canadian/Syrian dual citizen was deported to Syria by the US and tortured.
I was recently told by a US customs official that the US doesn't "recognize" dual citizenship. What gives?
It depends on exactly what is meant by "recognizing" dual citizenship. If the official meant to say that dual US/other citizenship violates US law, he was, simply put, wrong. If he meant that foreign citizenship makes no difference under US law if one is also a US citizen, he was right.
US citizenship law is primarily concerned with whether or not a given person holds US citizenship. If a person is a US citizen and is currently within the jurisdiction of the US, any other citizenship(s) he or she may hold are really not relevant in US law.
A "dual citizen" has no special status in the US by virtue of holding citizenship in some other country too. In particular, if you are a dual citizen and get into some kind of legal trouble while in the US, you should not expect the US to acknowledge any efforts by consular officials of your other country of citizenship to intervene in your behalf.
Also, when a "dual citizen" enters the US, he/she is expected to identify himself to US immigration and customs officials as a US citizen (not as a citizen of some other country) -- and in cases where a passport is required to enter the US, a dual US/other citizen is expected to enter on a US passport, just like any other US citizen.
I've heard of recent cases where dual US/other citizens briefly got into sticky situations while entering the US, when they attempted to identify themselves either as "dual" citizens or as citizens of another country. In former times (before the latest round of State Department policy reforms), attempting to enter the US on a foreign passport could even be used as "evidence" of intent to relinquish US citizenship. Although this apparently isn't a danger any more, the best thing to do is probably to make life simple and assert only your US citizenship rights when entering the US.
Remember that US immigration officers are primarily interested in determining whether a person wishing to enter the US should be let in. If you hold US citizenship, then you have a legal right to enter, remain in, and work in the US. Holding some other citizenship as well as US citizenship is completely irrelevant in this case, and if you make an issue of holding a second citizenship, you're just making it more likely that US officials will think something is amiss.