[murron]

If precedent has any bearing on this issue, then this link shows there were at least 6 presidents who were born in this country but whose parents were immigrants.

http://community.myvoa.com/_The-Seventh-US-President-with-a-Foreign-Born-Parent/blog/137360/45137.html

[chopperman]

That article does not provide precedence because it does not give the parents status at time of the birth. If they were naturalized, which I suspect they were, then those Presidents were Natural Born.