Wikipedia:

Article Two of the United States Constitution

Clause 5: Qualifications for office No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.

By the time of their inauguration, the President and Vice President must be:

<> natural born citizens (or citizens at the time of the Constitution's adoption) <> at least thirty-five years old <> inhabitants for at least fourteen years of the United States.

The Twenty-second Amendment also prevents a President from being elected more than twice.

The natural born citizen clause is a subject of debate. No law or court ruling has ever established the precise definition of a natural born citizen. It is generally agreed that a natural born citizen of the United States is any person born in one of the 50 states or the District of Columbia. But it is not firmly agreed[citation needed] if this definition should also include persons born in United States overseas territories or persons born to United States citizens living abroad. To date, no such person has been nominated for President or Vice President by a major political party, although some serious candidates for nomination (most recently George W. Romney, who was born in Mexico, and John McCain, who was born in the Panama Canal Zone) have fallen into the area of uncertainty. There is currently a movement to abolish the natural born citizen clause and allow immigrants to be President, thereby also eliminating the controversies regarding the definition of natural born. It has received exceptional support from California Governor Arnold Schwarzenegger who was born in Austria.

http://en.wikipedia.org/wiki/Article_Two_of_the_United_States_Constitution#Clause_5:_Qualifications_for_office