While shooting up my handloads this summer, I noticed that every brass was being marked with a scratch about 3/4" from the belt. This leads me to believe my chamber has a burr in it. Is there a simple proceedure the gunsmith can do to polish the chamber, or do I have to get it rechambered? I have a 300 WinMag.

David,
Yes, emery cloth on a dowel that is split in the middle. Dowel in an electric hand drill. Spin and polish the chamber.

It if is a M700, this is very common in new guns, I have repaired several. The burr is just ahead of the belt, where the belt recess ends and the chamber wall starts. Caused by a failure to deburr the chamber mouth at the factory!!! You can get rid of some of it by polishing as Chris suggests, but you will still have a sharp edge at the junction of the chamber and belt recess. I pull the barrel and put it in the lathe, takes about one minute with a deburring tool to put a nice small chamfer in the right place.

Be careful if you polish the chamber with emery cloth, too coarse a grit combined with a little side loading and you will egg shape the chamber mouth.

Part of a chambering job is to properly place a small chamfer at the chamber mouth to aid feeding and prevent case scratching. Sadly the manufacturers do not think this is necessary.