Jet drill press excessive runout

I recently bought a used Jet JDP-17MF drill press off of Craigslist for 1/2 of new price. When I began to use it I thought that I noticed that the bits in the chuck wobbled a bit more than I would like.

I got out a dial indicator and found that the amount of runout varies widely depending on where I measure. Above the chuck, on the arbor, just below the bearing, the runout is about 3 to 5 thousandths. On the chuck, just above the jaws, the runout is about 5 to 8 thousandths. On a bit that is chucked in the drill the runout is about 5 to 8 thousandths at the top and as much as 2 to 3 HUNDRETHS at the bottom or cutting edge of the bit.

From this I’ve come to the conclusion that my problem is in the chuck itself, not in the quill, the arbor, or the bearings. Does this sound correct? Which parts do I need to replace in order to correct this problem?

Thanks