I found this at the U.S. Dept of State website.
Acquisition of U.S. Citizenship By a Child Born Abroad
Birth Abroad to Two U.S. Citizen Parents in Wedlock: A child born abroad to two U.S. citizen parents acquires U.S. citizenship at birth under section 301(c) of the Immigration and Nationality Act (INA). One of the parents MUST have resided in the U.S. prior to the child’s birth. No specific period of time for such prior residence is required.
Birth Abroad to One Citizen and One Alien Parent in Wedlock: A child born abroad to one U.S. citizen parent and one alien parent acquires U.S. citizenship at birth under Section 301(g) INA provided the citizen parent was physically present in the U.S. for the time period required by the law applicable at the time of the child’s birth. (For birth on or after November 14, 1986, a period of five years physical presence, two after the age of fourteen is required. For birth between December 24, 1952 and November 13, 1986, a period of ten years, five after the age of fourteen are required for physical presence in the U.S. to transmit U.S. citizenship to the child.
I don’t know what BHO’s status is, but it would be worth looking into if I were Hitlery.