I see you have now changed your verbiage from "American citizen" to "natural born citizen" finally!
Natural Born Citizen as defined in The Obama File:
Both are U. S. Citizens AND Born in the U.S. mainland
US Constitution: Art. II, Sec. 1, Cl. 5
U.S. v. Wong Kim Ark, 169 U.S. 649 (1898)
Perkins v. Elg, 307 U.S. 325 (1939)
“The Obama File” is birther nonsense. Those cases don’t support what you claim.
Wong for example, quite clearly explains that a person born in the US is a natural born citizen.
"It thus clearly appears that, by the law of England for the last three centuries, beginning before the settlement of this country and continuing to the present day, aliens, while residing in the dominions possessed by the Crown of England, were within the allegiance, the obedience, the faith or loyalty, the protection, the power, the jurisdiction of the English Sovereign, and therefore every child born in England of alien parents was a natural-born subject unless the child of an ambassador or other diplomatic agent of a foreign State or of an alien enemy in hostile occupation of the place where the child was born.""III. The same rule was in force in all the English Colonies upon this continent down to the time of the Declaration of Independence, and in the United States afterwards, and continued to prevail under the Constitution as originally established."
United States v. Wong Kim Ark, 169 U.S. 649 (1898)
Except that Article II, Section 1, Clause 5 doesn't say that. Nor do the Elg and Ark decisions. Nor does federal law. And I've read them all.
In the US. It can be Hawaii, it can be most territories, or the Commonwealth of Puerto Rico. All those places are "within the country" which is the Vattel/"Law of Nations" definition. IMHO, even someone born in American Samoa, of US Citizens (which leaves out most Samoans) would qualify under the Vattel definition.