Is Barack Obama a Dual Citizen? US & UK/Kenyan?

Initial disclaimer: I have no doubt that Mr Obama was born in Hawaii and is eligible to be President of the United States.

My question is whether he is now, or ever has been, a dual citizen, with either British or Kenyan citizenship, via his father, a Kenyan. Since Obama Jr was born in 1961, while Kenya was still a British colony, was his father a British subject? If so, did he pass that status to his son? and did the independence of Kenya in 1963 have any effect?

factcheck.org is a great resource for checking claims and counterclaims in American politics. Here’s what they say:

Lots more detail over there.