If Ms. Dunham, a natural-born citizen, is his mother, then he is a citizen, regardless of where he was born.
It might be argued he isn't a "natural-born citizen," since that term has never been precisely defined legally, but he is most certainly a US citizen.
Of course, I haven't seen any DNA evidence she's actually his mother. But then, AFAIK, nobody has seen any for Bill Clinton, John McCain or Sarah Palin. How do we really know any of these individuals weren't born outside the US and smuggled in?
Not true. Under the law as it existed in 1961, if Stanley Ann was married to BHO Sr, and if BHO Jr. was not born in the US, then BHO Jr. was not a US Citizen at birth. The could have been naturalized later of course, but then he would not then be "natural born" by anyone's definition.
However if Stanley and and BHO Sr were not married, and BHO Jr was born overseas, or of course in the US, then BHO was a citizen at birth. If born in the US and BHO Sr. acknowledged paternity, as by being married to the mother, or otherwise, then BHO Jr is not "Natural born", because one of his parents was not a Citizen at the time of his birth. Only if someone else is the acknowledged sperm donor might BHO Jr have been natural born. That is having two US citizen parents and being born on territory under US sovereignty.