https://travel.state.gov/content/travel/en/international-travel/before-you-go/travelers-with-special-considerations/Dual-Nationality-Travelers.html says that dual citizenship is allowed. From that page:

How Do You Get Dual Nationality?
…
Naturalizing as a U.S. citizen while keeping the nationality of another country.

Wikipedia says:

Since 1990, the State Department has allowed multiple nationalities.[130] Official policy is one of recognition that such a status exists, but the U.S. government does not endorse a policy of having multiple nationalities, though it is permitted.[151]

https://en.wikipedia.org/wiki/United_States_nationality_law#Dual_nationality