How is it possible for Obama to be a citizen of Kenya and the US when that country doesn't permit dual citizenship? Obama might have been eligible for Kenyan citizenship, but according to this, his failure to renounce his US citizenship by age 23 would result in automatic loss of Kenyan citizenship.
If such a person wishes to retain Kenya citizenship, he/she is advised to renounce other nationality before the age of 23 years. Failure to renounce results in automatic loss of Kenya citizenship after age 23.
http://www.kenyahighcommission.net/FAQ2.html
I think he gets a pass here, the Kenyan citizenship had no force of law in the US, and as was pointed out up thread, to allow another country to declare someone is one of theirs leads to absurd scenarios, e.g. North Korea adopting John McCain as one of their own to keep him out of the White House.