John McCain faced the question. So did Barry Goldwater, George Romney, and Chester A. Arthur.
Their political opponents claimed they did not meet the Constitution's provision that "No person except a natural born citizen" can be president.
Now Donald Trump has said it could be a problem for Ted Cruz, who was born in Canada to an American citizen mother and a Cuban-born father.
The problem is, the Constitution does not define the term "natural born citizen."
Does it mean that someone must be born on US soil? McCain was born in the Panama Canal Zone. When Goldwater was born, Arizona wasn't yet a state. Romney was born in Mexico.
And Arthur? He was accused of being born in Canada.
The Constitution's drafters shed little light on what they meant by the phrase. It seems clear only that they wanted to make certain that whoever was elected president would be loyal to the U.S. alone and not to another country.
But the term "natural born citizen," many scholars say, was not in common use at the time the Constitution was written.
Even so, nearly every constitutional scholar who has studied the issue comes to the same conclusion: Anyone born to an American parent, no matter where in the world, is eligible to be president.
That conclusion about what the drafters meant is based partly on a law passed in 1790 by the first Congress, providing that the children of U.S. citizens born outside the country "shall be considered as natural born citizens." The law is no longer in effect, but it's considered evidence of the intent of the founders.
Then, in 1964, the Supreme Court muddied the waters by seeming to say, without deciding, that "natural born" meant born inside the United States.
In an opinion on an unrelated issue, the court observed, "The rights of citizenship of the native born and of the naturalized person are of the same dignity and are coextensive. The only difference drawn by the Constitution is that only the 'natural born' citizen is eligible to be President."
But that language is not legally binding, and the Supreme Court has never actually ruled on what "natural born" means.
Writing last year in the Harvard law Review, two former holders of the Justice Department's top courtroom advocate job — Solicitor General — said Cruz met the qualification.
"All the sources routinely used to interpret the Constitution confirm that the phrase "natural born citizen" has a specific meaning: namely, someone who was a U.S. citizen at birth with no need to go through a naturalization proceeding," Neal Katyal and Paul Clement wrote.
But until the Supreme Court rules on the issue, or the Constitution is amended, the issue will remain officially unsettled.