If the chuck is completely broken, you may not be able to tighten its jaws on a hex key. In those cases, the Single Wrench or No Wrench Method won't work.

On keyed chucks, if no other provision for gripping is present, you can use a hook spanner by locating the pin in one of the holes for the chuck key.

If you were born under a very lucky star, you might get away with fitting a chuck key and hitting that with a hammer at just the right angle. I did not tell you to do that.

A pipe wrench will grip just about any chuck, but at the risk of damaging it.

If all else fails, it is often possible to disassemble the drill, clamp either the chuck or the spindle in a vise and grip the other part with a pipe wrench or other gripping tool. This is very likely to damage the spindle and/or chuck though.