A Milwaukee drill is one of the premier drills made and is well respected for its reliability, durability and toughness. There are keyless chucks which need to be hand tightened, and keyed chucks which use an inserted key to enable maximum tightening and holding power, unmatched in a hand tightened application. Many times a keyless chuck might slip, and it may be time to change it out to a keyed version.
Tools for the Job
The basic tools you'll need to successfully remove your Milwaukee drill chuck are going to be a screwdriver--either a standard bladed type or a Phillips type, depending on the screw--a large Allen wrench, 3/8ths of an inch or larger, and a heavy mallet or hammer.
For safety purposes, always wear a good pair of safety glasses and gloves as a precaution when using these tools.
Removing the Keyless Chuck
Remove the set screw on the bottom of the keyless chuck. This will either be a Phillips or a standard head, so use the right screwdriver accordingly.
Insert the short end of your Allen wrench into the chuck and hand tighten as hard as possible. The long end should be sticking out from the side at about a 30 degree angle.
Place your drill on a bench or table, and looking at it from the front, determine which way is clockwise and counterclockwise. This is very important because the next step will be striking the protruding Allen wrench so that it spins counter clockwise. Give it a sharp strike with your mallet, and this will free up the threads so that you will be able to hand loosen the chuck and remove it.
Install the keyed chuck using the opposite procedure, and make sure the set screw inside is fully tightened down before you use it for drilling.