No, you definitely need to be US born to become President. Saying that they do amend the constitution 10 times a day so I suppose anything is possible.
As an afterthought - remember the film "Demolition Man" just after Sly Stallone is thawed out in the future he is taken to the Schwarzeneger museum. "Schwarzeneger museum?" he asks. "Yes" says the girl (Sandra Bullock as I recall), "Due to overwhelming public support the constitution was amended to allow him to run for President"
In July of 2003, Senator Orrin Hatch introduced a proposed amendment to the constitution to allow anyone foreign born and a resident for twenty years to be eligible for the office of President. Hatch and Schwarzenegger are old friends, and it is widely held that this amendment was a favor, should the governorship turn out to be a potential stepping stone as it was for the previous actor.