To replace the chuck of a Dewalt drill, you must first loosen and remove the chuck from the front of the drill motor. Before you loosen the chuck, you need to determine whether the chuck is removable. The task is easier than it first appears. Fully open the chuck and look down into the cavity in the center of the chuck. If you see a screw located where the chuck mates to the drill body, you will be able to remove the chuck. When there is no screw, you will need to send the drill to a repair shop to have the chuck removed.
Open the chuck of the drill all the way to access the locking screw located at the bottom of the interior of the chuck.
Slide the tip of the screwdriver down the interior of the chuck, into the head of the screw.
Turn the handle of the screwdriver clockwise to loosen and remove the screw from inside of the chuck. This screw has reverse threads, so turning clockwise loosens the screw.
Place the shorter leg of the Allen wrench into the chuck and turn the chuck clockwise to lock the Allen wrench into the chuck. Use the largest Allen wrench that will fit in the chuck, as smaller wrenches are more likely to bend. If the drill is a cordless model, set it to the "drill" setting with the clutch at highest resistance; this helps protect the drill's gearing as you loosen the chuck.
Set the drill on a work surface so the long leg of the Allen wrench is parallel to (and closest to) the drill handle. Alternatively, you can secure the drill in a bench vise, using a rag to protect the drill casing, being careful not to crack the casing in the vise jaws. Firmly strike the Allen wrench with the hammer to spin the wrench counterclockwise and loosen the chuck from the drill. If the chuck does not break free after the first hammer strike, repeat as needed until you can twist the chuck with your hand.
Loosen the chuck and remove the Allen wrench, then spin the chuck with your hand to remove the chuck from the drill.