There is a residency restriction if Obama was born outside the US under Title 8, subsection 1401.
§ 1401. Nationals and citizens of United States at birth
::snip::...a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years..
That is the 1986 statute. The 1952 statute that would have applied to Obama read "ten years, at least five".