I had the same problem, might not have been caused by the same thing, a small screw had fallen out of my chuck, the only solution was a new chuck, they make them so cheap that they don't have spares, just a replacement. Thats,as someone would say ,life.!
In the event that peanut is NOT joking, let's not try that. If you have not tried removing the chuck, try that. It just threads onto the power shaft of the drill. Then thread the same sized bolt into the chuck, secure in a vise or vice-grip pliers and attempt to loosen. If it doesn't work, I like allan.g0ias reply...
actually i wasnt joking, it has worked for me and the drill doesnt really run fast enough for it to hurt too much. the sudden force being applied to the chuck loosens it up. sorry it didnt work 4 you.