I sell a replacement Jacobs Keyless chuck for that drill for $42.99 this is not the Milwaukee chuck, but is as good or better. You could even replace with Keyed chuck if you want, just need one with 1/2-20 thread mounts. This is a very common chuck mounting thread, not like Milwaukee's other chucks which are 5/8-16
OK so looked at the 0300-20 that I have in stock and yes it is not possible to get at the hex portion.
In that case, I would start by (after removing the left threaded lock bolt that is) put a hex socket in the chuck and tighten it the best I could, even if only two jaws move and it is off centered, as long as it is tight. Then use an impact wrench and give it a whack. Gears are pretty robust and I have never broken any yet doing this.
If that does not work, then it is either, take a hacksaw or zip-cut to the boogered chuck and remove it in pieces, or remove the screws that hold the gearbox and grab the spindle shaft from the rear with split lock type clamp.
I usually go the first route, cut/break off the outer collar, remove any and all parts around and jaws. When you are left with just the chuck body cut it off just before the end of the spindle, you do not want to shorten the spindle! now cut alongside the threads of the spindle, again you do not want to cut into the threads. Flip 180 and cut off the other side. now you have two opposing flats that you can get a crescent wrench on. Whack the end of the crescent with dead blow hammer 9remeber right hand thread), If it still does not loosen then carefully grind a flat side until the threads just start to appear. Grip the two flats in the vise and hit just above the threads with a cold chisel and it should separate and then just slide off.
Walter