I am using the socket marked with a 0. Basically, the runout of the
chuck body gets transferred exactly to the runout of my test bar. So
the jaws are accurately holding my test bar, this does not seem to be
the problem. I am measuring runout on the chuck body and this is what
now reads .003". So it seems as if the chuck body is not seating
properly on the backing plate. The mating surface on the backing plate
was flat to around .0002" (measured farthest from the center). So I
imagine if the chuck were seated properly and the surfaces where
perfectly clean, which I took extra care to make sure, there should be
very little runout on the chuck body.

Also, I have not turned down the outside diameter of the backing plate
yet, so there is about a 1/4" lip sticking out past the chuck. When I
put my test indicator on this surface, which is the same surface the
chuck is mated too, it still measured around .0002" so I know the
backing plate is mounted properly to the spindle.

I still think the chuck may not be seating properly. I am not unhappy
with the set-up, but just not sure if this is typical from a Bison
chuck. As David mentioned, he was able to get his Bison 160mm (I
believe it is the same chuck I have) to .0005" TIR. So I am just
wondering if there were any other tips or techniques to getting the
chuck mated to the backing plate.

Thanks.