§ 1405. Persons born in Hawaii
A person born in Hawaii on or after August 12, 1898, and before April 30, 1900, is declared to be a citizen of the United States as of April 30, 1900. A person born in Hawaii on or after April 30, 1900, is a citizen of the United States at birth. A person who was a citizen of the Republic of Hawaii on August 12, 1898, is declared to be a citizen of the United States as of April 30, 1900.
O'Bama was born in Hawaii after April 30, 1990 and therefore meets the law for being a citizen. No need to have a parent reside a certain number of years, no restrictions on dual citizenship,....he just needed to take that first breath in Hawaii after 1990.
http://www4.law.cornell.edu/uscode/html/uscode08/usc_sec_08_00001405----000-.html
Correction-April 30, 1990 = April 30, 1900.