Since Kenya itself does not recognize dual citizenship, it would never have conferred Kenyan citizenship on someone born in Hawaii who is already an American citizen, even though the father had Kenyan citizenship. Therefore, Obama has only one citizenship - American.
Wrong.
From Obama's own website:
“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.”
That last sentence proves Obama jr was born a dual citizen thus voiding his natural born citizenship despite being born in Hawaii.
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."
http://www.uniset.ca/naty/BNA1948.htm
So Obama has British Citizenship at the time of birth, that is a given. Did he gain citizenship to Kenya? Yes - via Chapter VI, Section 87(2):
"(2) Every person who, having been born outside Kenya, is on
11th December, 1963 a citizen of the United Kingdom and Colonies or
a British protected person shall, if his father becomes, or would but for
his death have become, a citizen of Kenya by virtue of subsection (1),
become a citizen of Kenya on 12th December, 1963."
But did becoming a Kenyan Citizen terminate British Citizenship? We look into the Kenyan Constitution and find - NO, it did not. See Chapter VI, Section 95(1):
"95. (1) Every person who, under this Constitution or an Act of
Parliament, is a citizen of Kenya or who, under any law for the time
being in force in a country to which this section applies, is a citizen
of that country shall, by virtue of that citizenship, have the status of a
Commonwealth citizen."
So, like the Thai president recently who admitted he was part British at birth, Obama has never renounced his British Citizenship gained at birth. He never 'automatically' lost it, even when Kenya became independent.
The situations are basically identical.