Many wonder if becoming natualized as a British citizen means losing US citizenship. This is NOT the case
as shown below.
U.S. law does not require a person entitled to more than one nationality to give up his/her other nationality. Travel on a foreign passport does not affect U.S. citizenship. However, please note that all U.S. citizens, even dual nationals, must enter and depart the United States on U.S. passports.
http://www.usembassy.org.uk/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.
Countries usually do not like to tell you that you are entitled to dual citizenship. As a US citizen, you are perfectly entitle to acquire another nationality and keep your US citizenship.