If you're intending to keep the caliber the same, buy a new barrel. By the time you mess around finding a place that will do what you're thinking you want you'd have spent probably less money and a lot less time buying a new barrel and having a local gunsmith install it (if you can't do it yourself).
Now, I do remember hearing of someone on this board taking an old 9.3x57 rifles and having the bore increased from .366 to .376 and then had the chamber reamed for .376 Styer. If you're thinking of maybe doing something similar, but only going from .311 to .323 (8mm) and then chambering it for something unusual like 8x68, or 8mm-06 then that might be worth it from the "fun project" perspective.
