This is a question that has plagued me for quite some time. Chuck Norris is no pushover. He doesn't sleep... He waits. Even Batman sleeps, occasionally.
This is how the fight would go down...
Batman, seeing Chuck Norris as a potential threat to Gotham City as the city enters a second Quake much like the one in NML, due to Norris' roundhouse kicks, goes after Chuck with the Batplane. The plane crashes in Norris' beard, which we all know is indestructable. Batman, however, manages to escape.
Seeing the raw power of Norris' being, Batman enlists (Or forces, rather) the aid of Superman. Superman does everything he can to defeat Norris, but Norris simply laughs in his face and points out the face that the fist in his beard is 98% Magic, and 1% Kryptonite, Killing Superman instantly.
Before Batman can counter with enough time for preparation and study, Norris causes a massive earthquake near Wayne Manor, making the entire foundation fall ontop of Batman, turning him into human paste. Alfred too. And Stephanie Brown, since she finds some crappy way to come back by the time this story takes place. But no one really cares about that.
Norris by a beardhair.