Hi Danny,
I would first check that the chuck housing / body runs true then I would strip it bare so only the chuck body is left then mount it back on the lathe and see if the problem gets any better – if it does then the problem is with the parts left on the bench and if it doesn't it is time to take a real close look at the chuck body .
The casting could be thicker in one spot or it could have casting faults (voids ) that were not picked up on at the factory .
If it is the chuck body then I would then make a mandrel out of steel ( either turn one up or use silver steel ) then drill centres that run true in each end .
Then set this mandrel up in the four jaw chuck so it runs true and make sure there is enough sticking out of both ends of the chuck to allow mounting between centres
if you then mount up a dead centre in the spindle and one in tailstock you can use the lathe as a crude balancing jig by running this mandrel between centres loosely give it a spin and look for the heavy spot .
You can use small discs of steel held on with supa glue to play around adjusting the light spot to get it in balance and it is then a matter of removing the same weight of material from the heavy side , either way it will at least show you where the heavy and light spots are .
By using steel to add weight to the light Side that is round and of a know thickness ( a disc shape ) it would be easy to use an end mill of the same diameter to plunge cut to the same depth as the metal disc thickness to remove the equivalent amount of material from the heavy side
Ian