Do you need just a chamber, or do you also need feed ramps and the bolt shroud recess cut?
If you need the whole meal deal, most M14 smiths aren't even set up for the job. It also has to be perfectly indexed with the gas pot and sight splines - not for the feint of heart.
To do the job properly, you need a large knee mill with a vertical rotary table and a mounted 4 jaw chuck. The milling head is rotated 90 degrees and you cut the bolt recess with a ball cutter end mill and then plunge-cut the feed ramps after with the cutter set at an angle. I'd have to go check the drawing, but I think it's around 45 degrees. Prior to doing that, you need to align the barrel in the chuck so that the sight splines would put the front sight at top dead centre so you rotate the barrel to known coordinates for the cuts in accordance with the M14 barrel drawing.
You only chamber the barrel using a .300" live centre pilot roughing reamer AFTER the other operations are completed.
Hopefully all that work is already done and you just need a chamber. Anyone with a lathe and a roughing reamer can short-chamber a barrel for you.
Lastly, if you also need it threaded, it's an interesting experience cutting an indexed square thread on a manual lathe
For what it's worth, I've never personally done this particular job, but have seen it done in person at Crane Naval Surface Warfare Centre. It takes a real craftsman.
The mass producers use a CNC machine for a reason.
