Is Koran-Burning Protected by the First Amendment?

In a recent interview with ABC News, Justice Breyer questioned whether burning a Koran would necessarily be protected by the First Amendment.  Some excerpts:

“Holmes said [the First Amendment] doesn’t mean you can shout ‘fire’ in a crowded theater,” Breyer told me. “Well, what is it?  Why?  Because people will be trampled to death.  And what is the crowded theater today?  What is the being trampled to death?” . . .

“It will be answered over time in a series of cases which force people to think carefully.”

I’ll defer to Eugene on this question, but I’m particularly skeptical of the idea that the First Amendment would protect flag burning but not Koran burning (not that I’d recommend either, save burning a flag for proper disposal).

[Thanks to "Volokh Groupie" for the pointer.]