The supreme court interpretation of the US constitution.
Here is the Tribe/Olson opinion on the issue:
Per request from Senator McCain two researchers presented a report on March 19, 2008, declaring McCain to be eligible.
The Constitution does not define the meaning of “natural born Citizen.” The U.S. Supreme Court gives meaning to terms that are not expressly defined in the Constitution by looking to the context in which those terms are used; to statutes enacted by the First Congress, Marsh v. Chambers, 463 U.S. 783, 790-91 (1983); and to the common law at the time of the Founding. United Suites v. Wong Kim Ark, 169 U.S. 649, 655 (1898). These sources all confirm that the phrase “natural born” includes both birth abroad to parents who were citizens, and birth within a nation’s territory and allegiance. Thus, regardless of the sovereign status of the Panama Canal Zone at the time of Senator McCain’s birth, he is a “natural born” citizen because he was born to parents who were U.S. citizens.
and
Indeed, the statute that the First Congress enacted on this subject not only established that such children are U.S. citizens, but also expressly referred to them as “natural born citizens.” Act of Mar. 26, 1790, ch. 3, § 1, 1 Stat. 103, 104. and
Historical practice confirms that birth on soil that is under the sovereignty of the United States, but not within a State, satisfies the Natural Born Citizen Clause. For example, Vice President Charles Curtis was born in the territory of Kansas on January 25, 1860 — one year before Kansas became a State. Because the Twelfth Amendment requires that Vice Presidents possess the same qualifications as Presidents, the service of Vice President Curtis verifies that the phrase “natural born Citizen” includes birth outside of any State but within U.S. territory. Similarly, Senator Barry Goldwater was born in Arizona before its statehood, yet attained the Republican Party’s presidential nomination in 1964. And Senator Barack Obama was born in Hawaii on August 4, 1961 — not long after its admission to the Union on August 21, 1959. We find it inconceivable that Senator Obama would have been ineligible for the Presidency had he been born two years earlier.