This is not the first chuck I've replaced, but last time there was a spindle lock which made life easier. The screw is out but I'm having no joy with smacking the allan wrench, but I haven't gone to the bigger hammer yet.
On this older milwaukee drill there is a hex portion of the shaft below the chuck. I can't tell whether this is part of the chuck and should come off, or is it part of the shaft and I could put a wrench on it to lock the spindle. I can't read the model number, the closest manual I could find on the milwaukee site just gave the typical instructions with no mention of the hex section. It looks like if that weren't there the new chuck would end up too close to the body of the drill, so I kinda suspect it doesn't come off.
-Leuf