Well, remember that ANY amount of eccentricity registered on your tailstock will be DOUBLED in chamber size when you do a chamber reaming operation. That would total a 0.001" oversize chamber. The same is true for any lateral tailstock offset you might have from turning tapers, or whatever. The tailstock natchurly needs to be as centered as possible with the headstock center.
The way to get around that "oops" is pretty simple:
P.O. Ackley wrote that you ALWAYS do chamber reaming work with the berrel between centers, and drive the muzzle end using a dog. Support the chamber end on a steady rest. You do your rough chambering using the tailstock handwheel to drive in the reamer, with plenty of frequent withdrawls, cleaning, and lubrication, of course. Pressure lubrication from the muzzle is even better. Cut the chamber to say within 0.050" of full chamber depth. After that, use the tailstock center to GUIDE the reamer, but hold it with your hand in a glove.
Chambering this way will assure that you are not cutting the chamber oversize due to headstock/tailstock misalignment.