Push the drill's direction indicator to reverse. Hold the drill chuck with one hand, and depress the trigger with the other to open the chuck and remove the bit in the chuck. Keep rotating the chuck in reverse until it won't open any farther.
Insert an Allen wrench through the opened jaws and into the back of the chuck. Loosen and remove the screw by rotating it clockwise.
Grab the chuck with your hand once again, and depress the trigger with the other hand to loosen the chuck from the drive shaft. If you cannot hold the chuck with your hand, hold it tightly with a pair of wide-jaw locking pliers.
Rotate the chuck in reverse off of the threaded drive shaft, and set the old chuck aside.
Thread a new chuck onto the threaded drive shaft until it is hand tight.
Insert the screw you removed in step 2 through the opened jaws of the new chuck, and tighten it into the drive shaft with the Allen wrench.
Test the drill chuck by inserting a bit and tightening the jaws onto the bit.