The Act does not require one to renounce his or her US citizenship. Also, there is no prohibition against dual citizenship in the US.
The US Supreme Court, as early as 1952, has stated that dual citizenship is a “status long recognized by law” and that “a person may have and exercise rights of nationality in two countries and maybe be subject to the responsibilities of both. The mere fact he asserts the rights of one citizenship does not mean that he renounces the other” (Kawakita v US, 343 US 717). In 1964, the US Supreme Court also ruled that a naturalized US citizen has the right to return to his country of origin and resume his former citizenship while remaining a US citizen, even if he never returns to the US (Schneider v. Rusk, 377 US 163).