The U.S. Supreme Court did something Jan. 5 that it’s never done before, at least in modern times: It granted a law professor’s request to argue as an amicus curiae.

The Supreme Court regularly allows third parties to file “friend of the court” briefs to highlight aspects of a case neglected by the parties.

The high court, though, is more protective of oral argument time. The court—with one big exception—usually turns away third parties seeking to participate in oral argument.

The vast majority of amici don’t even bother asking to participate in oral argument, Brian P. Goldman, of Orrick,...