William Osborne, convicted in a brutal attack on a prostitute in Alaska 16 years ago, says a blue condom holds evidence of his innocence or confirmation of his guilt.
Either way, he says, the Constitution gives him the right to test the genetic evidence to find out.
The Supreme Court was to hear arguments Monday on Osborne's case and announcing whether it has accepted any new appeals.
More than 230 people have been exonerated based on DNA tests performed years after their convictions, according to the Innocence Project, a legal group that has sought genetic testing on behalf of hundreds of prison inmates and led the charge to free those who were wrongly convicted.
In many cases, eyewitnesses picked out the wrong man, often with the victim of one race incorrectly identifying someone of a different color. Among the exonerated were people who confessed to crimes, even though they were innocent.
The woman in Alaska was raped, beaten with an ax handle, shot in the head and left for dead in a snow bank near the Anchorage International Airport. The condom that was found nearby was used in the assault, the woman said.