I went through the naturalization process, most likely the same process that Linus Torvalds went through. When you take your Oath of Allegiance, you swear to renounce all foreign affiliations. However, the US government does not check that you actually go through with that formally. Since many countries do not revoke your citizenship upon you acquiring another, most naturalized people do hold dual citizenships.

As far as I know, Uncle Sam only gets pissed when you acquire another citizenship after you are already an American (either by birth or by naturalization). Even so, there are provisions in the law that account for the situation when a second citizenship is bestowed upon you without you actively requesting it (some countries do that automatically when you marry one of their citizens)