I replaced the chuck on my cordless Craftsman drill by first removing that screw inside the chuck, which happened to be reverse threaded, and then I inserted the short end of a 1/4" Allen wrench into the chuck and tightened it down, and then I held the drill up in the air in front of me, and then smacked the long end of the Allen wrench quickly with a hammer causing the chuck to turn counter clockwise fast enough to loosen it from the drill's drive shaft so that I could finish unscrewing it by hand afterwards. The trick is to jar the chuck quickly enough to loosen it from the drive shaft's threads since it is tightened down, and if you try to unscrew it slowly, then it won't work because the drive shaft moves too. When you install the new chuck, you just reverse the process. Smack the long end of the Allen wrench again but in the opposite direction to tighten the chuck and then secure it in place with that screw.
Mark, October 2008