http://travel.state.gov/content/travel/english/legal-conside...
but only if the act is performed (1) voluntarily and (2) with the intention of relinquishing U.S. citizenship.
Is the key point.
http://www.richw.org/dualcit/ - start here
http://www.richw.org/dualcit/faq.html - the meat of it is here
If you become a U.S. citizen, you're expected to renounce your other nationalities.
Edit: The biggest case was Facebook co-founder Eduardo Saverin renouncing U.S. citizenship for the tax savings
http://en.wikipedia.org/wiki/Eduardo_Saverin
2nd Edit: some discussion on Hacker News
https://news.ycombinator.com/item?id=3979669 https://news.ycombinator.com/item?id=4416258
http://www.immihelp.com/citizenship/dual-citizenship-recogni...
"“I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen…” from the Oath of Allegiance "
http://www.newcitizen.us/dual.html
apparently it is not binding:
" the oath has never been enforced to require the actual termination of original citizenship"
http://en.wikipedia.org/wiki/United_States_nationality_law#c...
Edit: can you ask your family if they took that oath, or is the information obsolete? Until now, I thought it was an actual requirement to renounce other citizenships.
Source: happily kept both passports.
Check out Belize and Costa Rica. Neither country will tax you at all. You even will qualify for a special residency visa!
Greeting from Greece!