Disconnect the drill's electrical cord from the power outlet. If the drill is a cordless model, remove the battery from the drill.
Insert the chuck key into one of the holes on the side of the drill's chuck, aligning the gears on the chuck key with the gears on the chuck. Rotate the chuck key counterclockwise to loosen the chuck.
Remove the drill bit from the chuck's jaws (if one was installed). Rotate the chuck collar counterclockwise as far as it will go, until the jaws are completely recessed within the chuck.
Insert an Allen wrench in between the opened jaws, and into the screw in the back of the chuck. Rotate the screw clockwise and remove the screw.
Place the drill flat on a work table. Insert the chuck key into one of the holes on the side of the chuck, and tap the chuck key with a rubber mallet, turning the chuck in a counterclockwise direction to knock the chuck loose from the drill's drive shaft.
Remove the chuck key from the chuck, and rotate the chuck counterclockwise to remove it from the threaded drive shaft.