You don't, but it's a common misconception. It's strongly recommended, though, as being stateless can cause all kinds of headaches.

Edit to prevent the inevitable doubters: http://travel.state.gov/law/citizens...nship_776.html

I think business people are the worst when it comes to uncritically repeating the mantras that are handed down to them from above. In many large corporations critical thinking is next to apostasy and anybody who asks the wrong questions is stamped as being obstructive and no team player.

In the past, the arts were often accused of being too touchy and wooly thinking but in my free time one of my little jobs on the side is an involvement in an academic pubishing organ. Although my role is purely technical I get to follow a lot of the other discussions and the bar appears to be quite high in terms of what gets published in arts subjects and what gets questioned and fundamental debates sometimes get sparked over very minor details. I have to raise my hat in awe of some the find minds who are asking the questions. The business world in which I have my main job never lives up to that standard of strict adherence to logic or turning the tables on those who try to appear smart by writing BS.

The State Department's content on the cited link does suggest that statelessness is an option, but every knowledgeable resource I've seen on the subject of renouncing US citizenship (e.g., here and here) has indicated that the State Department, as a matter of policy, routinely denies renunciations in the absence of a second passport.

You can certainly try it, and you may technically be right, but there's a difference between being right and getting what you want from a department of the US federal government, especially on foreign soil.

__________________
"Live every day as if it were going to be your last; for one day you're sure to be right." — Harry Morant

Interesting line

E. TAX & MILITARY OBLIGATIONS /NO ESCAPE FROM PROSECUTION

Also, persons who wish to renounce U.S. citizenship should also be aware that the fact that a person has renounced U.S. citizenship may have no effect whatsoever on his or her U.S. tax or military service obligations