Stuck keyed drill chuck

Put the drill in reverse, firmly grip the chuck (the part you were calling the head) and gently squeeze the trigger up the point that you cannot hold on. If you hear clicking, and it doesn't torque very much, you need to turn the torque setting up to the maximum (the highest number, or the drill setting if it has one). If it still doesn't budge and you're not able to hold the chuck against the force of the drill, you may want to use something stronger than your hand to hold the chuck. A strap wrench is well designed for this task and won't damage the chuck.

The chuck will most likely not be press fitted onto the shaft, meaning that hammering will not work to get the gap away.

the chuck actually screws onto the drill shaft (reverse thread - counter-clockwise to tighten) So what you need to do is the following:

1. Open the chuck fully, and look into the chuck opening - can you see a screw or Allen key? ... if so, remove the screw/bolt.
2. get one of your biggest Allen/hex keys and insert into the chuck (short side first) and tighten the chuck jaws around the key.
3. Turn the key clockwise until the chuck jaws are back to the original position.
4. Replace the screw/bolt.

if you cannot turn, you may want to place the drill on a hard surface and knock the key with a hammer a few times to see if it turns.