Depends:
A person born on or after November 14, 1986, is a U.S. citizen if all of the following are true:[7]
One of the person’s parents was a U.S. citizen when the person in question was born
The citizen parent lived at least five years in the United States before the child’s birth
A minimum of two of these five years in the United States were after the citizen parent’s 14th birthday.
Those are the rules for a child born abroad. Such a person is a citizen, but a naturalized one. This is because the person is a citizen by statute, and Congress, which passed the statutes, only has power over naturalization.
Prior to '86 the residency rules for the citizen parent were 10 years total, 5 of which needed to be ater their 14th birthday. If BHO was not born in the US he's not a citizen at all, because his mother had not lived in the US for 5 years after her 14th birthday.