Sure. Anyone born outside the US to an American mother or father, who had resided in the US for a certain number of years prior to the birth, is a lex sanguinaris natural born citizen. John McCain was born in Panama Canal, and that wasnt an impediment. http://en.m.wikipedia.org/wiki/Natural-born-citizen_clause
The first requirement is that you be a natural-born citizen of the United States. What a natural-born citizen is has been open for interpretation for a long time, but basically as long as a person is born a U.S. citizen, they meet the first eligibility requirement. A child born to U.S. parents abroad could rightfully be considered a natural-born citizen.
It is possible for one to become a president of the United States despite having not been born there. As long as one is currently legally an American citizen, he has a right to contest for the seat of the president.
It is totally against the law to become president or even be in the Senate if you were not born in the U.S. Which is one reason to impeach the president. His birth certificates are phony, and the experts have proved it. He was born in what is now Kenya.