If you go by the original intent, which is explicitly laid out in the Federalist Papers, not the interpretation, yes, he would be eligible, his parents are naturalized citizens who GAVE UP the allegiance to their birth country to become AMERICAN citizens AND he was born here!
If he were a Democrat he would be eligible, but being a Republican presents problems.
But they were not citizens when Jindal was born. They were Indian citizens and, according to India Citizenship Act of 1955, Jindal was also a citizen of India by birth.