footfootfoot:
I have that same chuck on my drill press. If I was in your situation, the place I would look first is at the alignment of the jaws. busterb's excellent link to jacobschuck led me to this conclusion. All three jaws have threads on them that correspond to one third of the circumference. If you check the jacobschuck link and look at the page called Service and Repair, you'll see a good diagram of what I'm talking about. If one of these jaws gets misaligned, it would feel like it was cross threaded (but with possibly only one third or two thirds being fouled up). That sounds like your description to me. So, one check would be to close the chuck fully and compare the tips of the jaws. Are they all the same height? Do they meet up squarely? If not, then you may have to disassemble, correct and reassemble your chuck.
FYI, here's a link I found that has
38% of the world's know reserves of talk about chucks. I fell asleep about 3/4 the way through. I did enjoy the story about the fella that repaired his seized diesel piston in Tahiti with dry ice and a propane torch, though. Entertaining and possibly useful, but I didn't see a bullseye answer to your question.
I would also like to know how your chuck comes off. Does it have a screw inside? Is it on a tapered shaft?