I watched a highly regarded maker of custom rifles who chambered his barrels by simply grabbing it in the three jaw chuck and reaming the chamber. He counted on his Clymer reamer holder to follow the bore; it didn't. The thing that got me was, he was a good machinist and he knew better.
Anyway, when I first started gunsmithing, I was taught to set the barrel up between centers to true the shank, turn the tenon, and thread it. Then, the barrel was held in the three jaw, at the muzzle end, and the shank was supported in the steady rest. If the center cut at the breech end of the barrel was cut concentric, if one used a dead center in the tailstock, and if the barrel was pretty straight, this method could produce a good result. Many gunsmiths still use this technique, and it is still a viable method, most of the time. It is popular for guys who are turning out a lot of barrels, because it is fast. Doing it this way, I have fitted, chambered, polished, stamped, and beadblasted, 6 barrels on 6 different actions, in one eight hour day. This on an old South Bend lathe. I was helping out a barrel-maker friend of mine and this was his preferred method, so this is how I did it.
One gunsmith I knew would turn and thread the barrel between centers, then hold it in a four jaw to chamber. He dialed in on the outside, and assumed the shank was co-axial with the bore since he had turned it between centers.
Another made a steady rest which featured a pair of tapered roller bearings and 4 screws which allowed him to dial in the bore. The steady was adjustable so he could be sure it was aligned with the tailstock. It was quite an ingenious set-up and it worked pretty well for him.
In general, I think dialing in the throat area and the muzzle, then pre-boring, is one of the better ways to do a chamber. Every method works best when the barrel is perfectly straight (uncommon) and many methods have come about from having to deal with barrels which are not quite straight or, in some cases, damn crooked! WH