http://travel.state.gov/travel/cis_pa_tw/cis/cis_1753.html
A U.S. citizen may acquire foreign citizenship by marriage, or a person naturalized as a U.S. citizen may not lose the citizenship of the country of birth.U.S. law does not mention dual nationality or require a person to choose one citizenship or another. Also, a person who is automatically granted another citizenship does not risk losing U.S. citizenship. However, a person who acquires a foreign citizenship by applying for it may lose U.S. citizenship. In order to lose U.S. citizenship, the law requires that the person must apply for the foreign citizenship voluntarily, by free choice, and with the intention to give up U.S. citizenship.
The U.S. Government recognizes that dual nationality exists but does not encourage it as a matter of policy because of the problems it may cause.