You have a indicater by the sounds of your post. So here is the way I would start.
Remove the chuck from the back plate. Run the indicater on the face the chuck would be against. If it shows run out. Remove from spindle and clean with a tooth brush sized s/s brush, make certain no chips or swarf are in the threaded area. Reassemble check again, still have run out? You would need to leave the backing plate in place, and take a very light skim cut. I would start at the register step, and feed out wards toward the operater.
The next thing to check before you cut anything is the register step. This is the step that fits in the back side of your chuck. Now if you have allready removed the chuck, was it a snug/tight fit? or just fall right off? Either way, get the tip if your indicater on that step, check for run out. If you have run out on either of these places will cause you problems.
Other things to look for, raised treads at the back of the chuck. These can be stoned down flat. Stoning the back of the chuck looking for raised spots, should be done anyway. Look at your back plate closely for embedded chips that might hold the chuck out from the backing plate too.
You may need to take a facing cut to the back plate to true it. Also you may need to take a skim cut to the register as well if need be. If the chuck is loos on the register allready, mount the chuck, and indicate they body of the chuck, and use a dead blow hammer to shift the chuck for the min run out whiie the bolts are snug, and not tight. You can bump it around to get the min run out on the body. Once you get this far, you should have a pretty good indication of how true it is. Run the indicater on the body, and the front face.
If you can get all this sorted out, then chuck up a known piece of true running stock, and you guessed it, chck run out again. But ,,, you have dissasembled this chuck, and cleaned the scroll and all related parts first. and chips in there will affect your reading once again! Once the scroll and all related parts are cleaned, and still have bad runout. I would look for tell tale signs of a crash, if none show up, then I would haul out the toolpost grinder, or rig up your own, and regrind the chuck jaws on the lathe, but that may be past your abilitys at this point. So, get to checking this stuff out!
Good Luck