The lawsuit claimed he should be disqualified because, it claimed, he acquired the same British citizenship that his father had when he was born.
This meant he was not a "natural-born" US citizen, as the US constitution requires, it alleged.
Mr Obama's birth certificate shows he was born in Hawaii.
The issue was addressed by Mr Obama's aides during his presidential campaign, when they posted online his birth certificate - which was verified by
This lawsuit, brought by retired New Jersey lawyer Leo Donofrio, gained a high profile because it was distributed by Supreme Court Justice Clarence
Thomas to other justices for discussion.
It conceded that Mr Obama was born in Hawaii - but contended that he still held foreign citizenship at birth.
It read: "Since Barack Obama's father was a citizen of Kenya, and therefore subject to the jurisdiction of the United Kingdom at the time of Senator
Obama's birth, then Senator Obama was a British citizen 'at birth', just like the framers of the Constitution, and therefore, even if he were to
produce an original birth certificate proving he were born on US soil, he still wouldn't be eligible to be president."
Kenya was part of British East Africa until it received its independence in 1963.
A decision not to grant a writ of certiorari - the legal term for the declaration that the justices will hear the case - means that a lower court
ruling that dismissed the lawsuit can stand.
Can we please stop this debate now, for all the people that dont want him to be president tough no more moaning about his eligibility
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