How can I repair the chuck on my cordless drill?
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:


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