Not in the public realm, of course.
However, this is available:
Barry's Parents Divorce:
The 1964 divorce record from the Circuit Court of the First Judicial Circuit State of Hawaii, states that Stanley Ann D. Obama and Barack H. Obama "were lawfully married in Wailuku, Maui, State of Hawaii, on February 2, 1961, by a person duly authorized to perform marriage cerimonies and ever since that date have been and are now husband and wife."
http://www.scribd.com/doc/18130289/Obama-1964-Divorce-Papers-13-Pages-Missing-Pg-11
“were lawfully married in Wailuku, Maui, State of Hawaii, on February 2, 1961, by a person duly authorized to perform marriage cer[e]monies...”
My limited understanding is that to make a marriage lawful, the “duly authorized person” must sign and date the marriage license, and file it within a set number of days with the clerk of the county court in which the marriage occurred. The clerk books the original, making the marriage “lawful” and “of record,” and prevents forging documents after the fact (to steal an inheritance for instance).
Lots of questions:
Searches for the records were reportedly unsuccessful. Why? No marriage records kept in Maui in 1961? Records kept but large sections now missing? Or, just this record missing?
Would it be possible to record the license in some other county, even if the marriage ceremony supposedly took place on Maui? (Seems bogus, but anything seems to go in HI).
Is it known if anyone has checked for such a public record in Oahu?