Where ever Obama was born, he was a British Citizen at the time of his birth by virtue of his father being a British Citizen.
As a Kenyan native, Barack Obama Sr. was a British subject
whose citizenship status was governed by The British Nationality Act
of 1948. That same act governed the status of Obama Sr.’s children:
“British Nationality Act of 1948 (Part II, Section 5): Subject to the
provisions of this section, a person born after the commencement of
this Act shall be a citizen of the United Kingdom and Colonies by
descent if his father is a citizen of the United Kingdom and Colonies
at the time of the birth.” In other words, at the time of his birth,
Barack Obama Jr. was both a U.S. citizen (by virtue of being born in
Hawaii) and a citizen of the United Kingdom by virtue of being born to
a father who was a citizen of the UK. Obama’s UK citizenship became an
Kenyan citizenship on Dec. 12, 1963, when Kenya formally gained its
independence from the United Kingdom. The court noted that Chapter VI,
Section 87 of the Kenyan Constitution specifies that:
In other words, all the rest is immaterial.