According to his Grandmother in Kenya, the answer is "No." In an interview with Israel News, Barack Obama's grandmother, half-brother, and half-sister all claim that he was born in Kenya.
Now, there is another odd piece of evidence pointing to this claim. Obama's birth certificate from Hawaii has been proven false by many different sources.
The Times Herald even reports: "the senator's grandmother, brother and sister, who live in Kenya, believe they were present during Obama's birth in the African country." Here, the Times Herald uses the word that his family 'believe' he was born in Kenya (perhaps to avoid possible law suits by Obama's Truth Squad?).
The U.S. Constitution states, in order to be President of the United States, you have to be born here in the U.S. If these allegations are proven true, then Barack Obama can not be President.