The above solution should work if you have a fairly new driver, but, if you have a used and worn driver, this may not work.
My 2 drivers are worn as stated and the above method wouldn't work. When I tried to hit the allen wrench, it just turned the chuck, gearbox and motor as one solid unit. I then decided to try and cut the old chuck off with a dremel (didn't work because I got scared I'd cut into the threads).
The next set of instructions, or explaination of what I did, won't restore the drill to like new condition, but it will allow you to remove and replace the chuck.
Finally, I dismantled the entire drill. First by following the previous posters instructions for removing the left-handed screw that holds the chuck on. Then, take the six screws out that hold the housing together. The rest is feel as you go.
Once the motor is off and all the gears are out, you can get to the back of the shaft. I clamped a pair of vise grips onto the back of the shaft and clamped the vise grips into a bench vise. Next I took a small pipe wrench and twisted the chuck off.
If you decide to go this route, make sure you pay close attention to how it goes back together.
My drill works as it did before, a little noisier 'cuz I didn't lube the gears during assembly. But now it has a new chuck that'll clamp onto small drill bits again.
If you have problems with anything I stated, my email address is: mitymouse17@yahoo.com. If I don't get back to you, your email may have gotten caught by the spam filter (unlikely but possible).
Dave
July 2007