If you use your electric drill frequently, you may eventually have to remove the keyless chuck and replace it with a new one. Make sure you are using the correct replacement part for your drill before attempting to install it. Forcing the wrong type of chuck onto the spindle can damage the threads and could create a dangerous wobble when the drill begins to rotate at high speed. Take the old keyless chuck with you to the hardware store when shopping for a replacement, or check the manufacturer's website for the correct part number.
Disconnect the drill from its power supply. For a cordless drill, this will be a battery pack. For other types of drills, unplug the power cord from the electrical socket.
Press and hold the spindle lock button on the drill's body to release the chuck. Continue to hold the button down while turning the chuck counter-clockwise to open the jaws as wide as possible.
Look into the opening between the jaws. If there is a screw inside, loosen it with the appropriate type of screwdriver (flathead or Phillips).
Place a large Allen wrench between the jaws of the chuck. Press and hold the spindle lock button while turning the chuck clockwise until it is tight around the Allen wrench. Make sure the spindle lock button is fully disengaged before proceeding to the next step.
Lightly tap the end of the Allen wrench with a rubber mallet so that the chuck turns counter-clockwise. Continue to tap until the chuck is loose enough for you to twist it the rest of the way off the spindle with your hands.
If you are replacing your old chuck with a new one, make sure the replacement is properly seated before using the drill to work again. It can be dangerous for the chuck to rotate even slightly off-axis. Hold the drill up and briefly press the trigger to check the rotation of the drill bit before using it on any projects.