Cannot remove bit from chuck brother-in-law put a small phillips head bit in the chuck

There is supposed to be a Phillips head LH thread screw in the chuck. I have seen the screw head worn down so you can no longer get a screwdriver to work.
We usually cut the chuck off with a metal chop saw just at the screw - thread what remains of the chuck off, which usually leaves 1/4" of the screw sticking out of the spindle - remove with vise grips.
Its not an easy prospect when that happens.

It sounds as though you will have to replace the chuck. Remove the screw (l/h tread) from inside the chuck first before removing it.

check the inside of the chuck at the bottom(open the chuck to max). There should be small screw there with either a hex or a Phillips head. It is a left hand screw that locks the chuck in place and will not let it unscrew when you are removing parts.. If it is not there then you will have to get one from an old drill that is junk unless you can get one from an electrical appliance shop the repairs drills.

take flat head screw driver put flat head driver in to gears on chuck hit screw driver with hammer counter clock wise

Take a phillips screw driver and stick it into one of the key holes. Then take a flat head screwdriver and stick in one of the slots. And prise against the phillips.

Or you can wrap a belt or strap around the chuck hold it tight, then put the drill in reverse and unscrew it.

Drill a hole in the top of the phillips head screw with a 3/16 th's bit. Don't drill the head of the screw off, just drill deep enough for a torx bit to hold. Take a T-30 torx bit and tap in into the hole you have drilled. Then turn the screw clockwise and it should come out fairly easily.

Sounds like the bit bent slightly and as a result jammed into the chuck. Open chuck as much as possible and have someone pull the bit out while your tapping it with a small hammer. The vibration from the tapping might loosen the bit from the chuck.

It really depends on the model. Here is a general description of how to remove most regular keyed and keyless chucks from corded and cordless drills:
Some chucks have a Left Handed screw that secures them to the spindle so they do not come loose. You can look into the chuck with a flashlight and see if there is a chuck screw. (It may be a torx head, flat head, or philips head) You will need to remove this screw first before doing anything else. Sometimes there is loc-tite applied to the screw so it may be stubborn and sometimes you will strip the screw head. Remeber that the old saying lefty-loosey, righty-tighty does not apply here. Left is actually tightening a left hand thread, so you want to turn it right to loosen. I know, it will feel weird but thats the way to loosen it. You may have to apply some heat to the screw in order to get that loc-tite to break. A pencil torch works great. If you strip the head out you will have to use a drill press and drill the screw head off.
After removing the screw you can remove the chuck.
To remove the chuck, the easiest way is to use a hex socket bit and an impact wrench. Put the hex bit in the chuck, and depending on the condition of the jaws, tighten the jaws as much as possible to the hex bit. Put the impact in reverse and bump it until the chuck is loosened. If you do not have access to an impact wrench you will need to put a hex key with a long arm into the chuck and tighten it then place the drill on the edge of your bench and give it a good whack with a 3lb hammer. It may not come off immediately so you may have to reset and do this a couple of times. Not the most effective way to remove a chuck, especially if one of the jaws is missing, but that is what most manufacturers tell you to do. I myself cut the collar off with a die grinder and then use a pipe wrench on the body of the chuck applying constant pressure while heating the chuck body with a torch. Works every time. Heat is our friend on stubborn chucks. Good luck, any questions please post.

open jaws for large size bit.look in bottom and there will be a screw slot or phillips head screw or possibly an allen head screw.remove this,by possibly turning clockwise. and then chuck up a large allen wrench. try removing the chuck by tapping wrench with hammer. this may be threaded on counterclockwise.have to try both ways.

I HAD THE SAME PROBLEM AND STILL DO FROM TIME TO TIME. I USE THE PROPPER BITS, SO THAT ISNT THE PROBLEM.
WHAT WORKS IN GETTING THEM OUT... JUST TAP THE BIT INTO THE CHUCK AND THEN PULL THE QUICK RELEASE AND THE BIT COMES RIGHT OUT. THE BIT JUST GETS INTO A BIND AND TAPPING THE END FREES IT UP