The U.S. Constitution says someone must be born in the United States, among other things, to be president.
ABC News reported Democratic Gov. Neil Abercrombie told Honolulu's Star-Advertiser, "Our investigation is showing, it actually exists in the archives written down."
Abercrombie, a college friend of Obama's parents, told the newspaper, "What I can do, and all I have ever said, is that I am going to see to it as governor that I can verify to anyone who is honest about it that this is the case," adding that producing the document "has a political implication for 2012 that we simply cannot have."
ABC said it was unclear if the document in the archives was Obama's long-form birth certificate, but in any case it has yet to be produced. "Birther" conspiracy theorists say only the long-form certificate will prove Obama was born in the state.
In 2008, the Obama campaign released a "certification of live birth," a shorter document that carries the same legal weight as the long form.
But "birthers," among them Orly Taitz, say only the long-form certificate that includes the name of the hospital and the doctor, his or her signature, the baby's birth weight and the national origin of the parents will do.
Taitz once produced a Nigerian birth certificate for Obama that was widely dismissed as an obvious fraud. The "birther," who was born in the old Soviet Union, also has filed numerous lawsuits pursuing her theories.
ABC said the archives of two local papers, the Honolulu Star Bulletin and Honolulu Advertiser, have birth announcements for a young Obama son in early August 1961.
Even so, 14 percent of Americans say they think Obama was born in another country, the most recent ABC News-Washington Post poll indicates.