The Constitution spells out who is eligible for the presidency in Clause 5 of Article 2: 'No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.'
And the 12th Amendment extends those qualifications to the vice-president.
Left unexplained is what 'natural born citizen' means - and the phrase is defined in no other piece of legislation.
But the 14th Amendment of 1868 is also in the Constitution - and defines who is a citizen.
It says: 'All persons born or naturalized in the United States and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.'
In 1873 the Supreme Court ruled that the phrase 'subject to its jurisdiction' was intended to exclude children of non-citizen immigrants.
But that decision was in an arcane question - about whether the 14th Amendment only guaranteed rights to people who were U.S. citizens, and didn't cover anyone who was only granted 'citizenship of the state' by an individual U.S. state - in other words, were free to live and work there.
The majority opinion includes a note that 'the phrase "subject to its jurisdiction" was intended to 'exclude from its operation children of ministers, consuls, and citizens or subjects of foreign States born within the United States.'
Two years later the high court ruled that immigrants can only have automatic citizenship for their children when they – the adults – owe 'allegiance' to the U.S. and not to a foreign nation.
The concept of allegiance means little today but most people at the time were born in monarchies with limited rights and were subjects, not citizens - and until you became an American citizen, you were still owing allegiance to that monarch, it was argued. 'Allegiance' to a foreign monarch and being subject to American 'jurisdiction' were not compatible, the justices ruled.
But then in 1898 the Supreme Court ruled that a specific Chinese immigrant's child was a citizen of the United States, citing the 14th Amendment's text.
In the case, about Wing Kim Arg, the justices ruled that 'a child born in the United States, of parents of Chinese descent, who, at the time of his birth, are subjects of the Emperor of China, but have a permanent domicile and residence in the United States, and are there carrying on business, and are not employed in any diplomatic or official capacity under the Emperor of China' was automatically a citizen.
That ruling has been the bedrock of birthright citizenship - known as jus soli - and has led to the other opinions about the amendment being seen as being superseded - although they have never formally been overturned.
The dissenters - or in cruder terms, the losers - said the 14th Amendment and those who passed it intended citizenship to be only for those not claimed by any foreign power in any form, so natural-born citizenship was hereditary - a concept known as jus sanguinis.
Since then the Supreme Court has ruled that a woman born in New York to one U.S. citizen father but brought up abroad was eligible to run for president - she did not - but has never explicitly ruled on whether someone born to one or two non-citizens can.
The fact that scores of millions of Americans have been considered citizens by the federal government in exactly those circumstances would seem to suggest how the justices would rule.
But it leaves Kamala Harris 'birthers' a very narrow opportunity to argue that the Supreme Court has never ruled clearly that being born in the U.S. to non-citizen parents makes you 'natural born' - as opposed to simply a citizen.
One - in a Newsweek op-ed - claimed that because Mexican guest-workers' American-born children had been deported in the 1920s, 1940s, and 1950s - the idea of 'birthright citizenship' for all really dates from after Harris' birth.
He also claimed that it was unclear exactly what Harris' parents' legal status was and that if they did not have green cards, that might disqualify her too.
Harris, however, is not the first candidate to face questions over eligibility thanks to her parents.
Obama - as well as the bogus claim he was not born in the United States - faced ultra-fringe birther questions because his father was a Kenyan; and the oldest example was Chester Arthur, whose mother alone was American and who also faced questions over a rumor he was born in Canada, not Vermont.
Unhelpfully for birthers, none of those who faced these questions were successfully disqualified by any court - in fact, no challenge of the kind has ever succeeded.
Perhaps even more unhelpfully, the Newsweek op-ed writer, law professor John Eastman, previously campaigned for Ted Cruz, who was born in Canada to one U.S. citizen parent and a Cuban father, suggesting his claim that Harris might not be eligible was more politically expedient that constitutionally sound.