Hi HH, There is a limited amount you can do with a three jaw when it gets worn, but you can usually improve the situation somewhat. first, take the chuck off the lathe, strip it down, looking for any damage or looseness in the jaws and the scroll, clean it, oil it, and rebuild it. Check the lathe nose threads, and the register to for any damage or dings and if you find any, stone them off so you know the chuck is properly seated on the lathe, oil the thread and put the chuck back on the lathe. Get a known good piece of , say 1" plus dia bar, put it in the chuck, with the end right at the back of the jaws, tighten it firmly,and watch the jaws carefully as you do it to see if you can see the jaws rising in their slots and use a DTI to check the runout. Any better? If the chuck has adjusting screws adjacent to the backplate bolts, you need to slacken the backplate bolts very slightly, and adjust them to dial the chuck in on the DTI. If there is play between the register on the backplate and the chuck, you can slacken the bolts holding the chuck to the backplate, and bump the chuck with a hide mallet and see if you can improve it that way, or make a mark on the backplate and the chuck, then remove the chuck from the backplate and see if you get better concentricity by turning it one set of fixing holes, and refitting it. At the end of the day, you can put each job in the chuck, then bump it with a mallet and check with a dti, till you get it "near enough". remember a 3 jaw chuck will have 3 to 4 thou run out when new! Mine, on a Colchester Student mk1 ran out about 17thou, but with care, this could be reduce to about 6 thou which was adequate (barely) but I used it until I was able to get a new (to me) chuck! Don't sweat it, make what you want to make on it, and if the parts aren't accurate enough, look for another chuck. Can you post up some pics, of the lathe and the chuck, especially the side faces of the chuck so we can see if it has adjustment screws or not.
Good Luck,
Phil