Plug in the electric power cord to the power outlet on corded DeWalt drills. On cordless models, a charged battery must be installed into the drill.
Set the drill's direction indicator (found just above the trigger) to reverse. Hold the chuck firmly with one hand, and depress the trigger with the other hand. The motor should rotate in reverse, causing the chuck to loosen. Keep loosening the chuck until the jaws stop opening, as they are opened to their widest point.
Insert an Allen wrench in between the jaws of the chuck and into the screw at the back of the chuck. Rotate the wrench clockwise to loosen and remove the screw.
Hold the chuck firmly in one hand, and depress the trigger again to loosen the chuck from the drive shaft. If you cannot hold the chuck firmly enough to release it from the drive shaft, try holding the chuck with a pair of vise-grip pliers.
Set aside the damaged chuck and thread a new keyless chuck onto the drill's drive shaft. Twist the chuck clockwise until it is finger-tight.
Flip the direction indicator on the drill to forward, hold the new chuck firmly, and depress the trigger to tighten the chuck onto the drive shaft.
Open the jaws again. Replace the Allen screw into the hole in the chuck, and tighten it with an Allen wrench.