I have done this repair a few times with Good results on Milwaukee and Porter Cable Drills.

Method A
A lot of Jacobs type chucks have a retaining screw deep inside the chuck that is either a Torx or Allen socket pan head screw.
Normally it's a left hand thread so #1 find the correct tool
and #2 turn right as if tightening.
It should loosen up.
Be careful not to strip out the fastener head if it does not loosen Quit.
#3 Try turning normal left to loosen.
If it doesn't back out Quit before You strip the head.
#4 Now clamp it in a vice chuck up handle down.
Now give the inside and outside of the chuck a good soaking
of WD40 PB blaster, liquid Wrench, Deep creep or similar lube
and leave it overnight to let it soak.
Try step 2 then 3 again the next day.
Still no luck You could hold the chuck in the vice plug it in
and go forward and reverse back and forth.
If it budges repeat over and over it until You gain full opening and closing.
Method B
If it doesnt work properly check Your warrantee and if its good replace the drill.
If not buy another drill of Your own preference.
Method C
O.k. Say You succeeded in removing the screw inside.
This is good because inside the chuck is a female Morse taper.
The drill itself has the male end of the taper.
So You need to separate the taper friction fit.
Rap it apart by holding the chuck in the vice
Then tap the drill body the opposite way to separate the two.
If You succeed at this, You can soak the whole chuck in a small can of marvel oil .
Try it with your chuck key if unless it is a non key type.
If there is still no luck all is not lost .
Method D
Buy a replacement chuck True Value, Lowes, Home Depot.
You may have to go to the manufacturer website if the Box stores dont have one.
You will need Your manufacturer and model number of the drill .
The chuck may even have its own number stamped into it.
If You get one carefully compare all aspects of the new one against the old one.
If the tapers are not the same it will not work. Repackage and return the chuck.
If it is Correct Assemble the two tapers,
tap the chuck into the drill with a plastic wooden or leather hammer ,
then replace the hardware. Some chucks come with a new screw.
Check it and compare that is the same as the one you took out.
If its the same screw it in carefully.
There should be very little resistance.
If all is correct tighten it up .
You are Good to go

I hope you succeed this mission and save Your drill.
rick B.