[rxsid]

"I’d swear I grew up learning that to become a US citizen, one had to renounce all former allegiance.

To become a Naturalized citizen, one is required to:

"To become a U.S. citizen you must take the Oath of Allegiance. The Oath includes several promises you make when you become a U.S. citizen, including promises to:

• Give up all prior allegiance to any other nation or sovereignty;
• Swear allegiance to the United States;
• Support and defend the Constitution and the laws of the United States;
and
• Serve the country when required."

http://www.uscis.gov/files/article/M-476.pdf

[rxsid]

The actual oath (from the same link as above):

"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;
that I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic;
that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by the law;
that I will perform noncombatant service in the Armed Forces of the United States when required by the law;
that I will perform work of national importance under civilian direction when required by the law; and that I take this obligation freely without any mental reservation or purpose of evasion; so help me God."