While the constitution does state that to be president, one must be a "natural born citizen", it in NO WAY defines what that term means. So we are left with something of a legal void.
There is the Part of the U.S. Code that address this. His mother, Stanley Ann Dunham, being born in Kansas, was a natural born citizen (I don't believe there is any question on that point).
Section (e) of the code above stats:
(e) a person born in an outlying possession of the United States of parents one of whom is a citizen of the United States who has been physically present in the United States or one of its outlying possessions for a continuous period of one year at any time prior to the birth of such person;
So, regardless of where he was born (Hawaii or Kenya as some have claimed but provided little if any evidence), he is a citizen.
However, the U.S. Title only states that "The following shall be nationals and citizens of the United States at birth", and does not use the phrase "natural born".
There is no final, legal definition even today on what "Natural Born Citizen" means, according to legal professor Gabriel "Jack" Chin:
Unfortunately, the text of the
Constitution does not define natural
born citizenship, and neither the
Supreme Court nor Congress has weighed
in on the question.