4 Supreme Court Cases define "natural born citizen" http://www.thepostemail.com/2009/10/18/4-supreme-court-cases-define-natural-born-citizen/
Well, not really. That link and those cases make some good arguments but the definition itself is never made in a crystal clear manner.
In fact, there is this statement from the cases;
"These were natives or natural-born citizens"
...which further muddies the waters between the two terms. I'll admit a case could be made that one's parents would have to be citizens but just as good a case could be made to say native = natural. I doubt that any court or the American people would accept such a distinction. The legal and philosophical trend in America is just the opposite in fact.
In the end, Jindal is a citizen an if he runs no one of any reputation will challenge him. To do so would be to be called a birther (or in this case, what, a naturalizer? I dunno) except they'd be on shakier ground legally and popularly.