Quote from makloda:
Not if you give up your passport and sever all ties with the US.
http://travel.state.gov/law/citizenship/citizenship_776.html
Ok but this was what I was getting at (This has more to do with owing tax before you renounce citizenship):
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 (contact the Internal Revenue Service or U.S. Selective Service for more information).