The best answer is ask Shilen. This come from there web site.
http://www.shilen.com/

Located in the FAQs section.

CHROME MOLY STEEL BARRELS-- When re-barreling a rifle with a Chrome Moly Match Grade or Lone Star Grade barrel, the barrel must at some point be either blued or teflon coated to prevent rusting. We offer two blued finishes for chrome moly steel barrels. The blued options are polished and blued or glass peened and blued. The polished and blued finish is done by polishing the barrel with 180, 240, 320, and 400 grit sanding belts, finishing with a Scotch BriteTM polishing pad, and then bluing. A "glass peened and blued" finish is accomplished by first polishing the barrel with a 180 then a 240 grit polishing belt. The next step is to "peen" the surface by spraying it with fine glass beads under high pressure to dimple the surface texture to reduce the surface refection. Finally, it is blued. Action finishes are done in basically the same manner. Barrel finishes and action finishes are priced separately. To glass peen and blue the barrel and action will cost $60.00 for the barrel and $60.00 for the action, for a total of $120.00.

The problem is to get this the barrel would have to be custom ordered, from Shilen, and you now into a long wait period. Mass majority of people get barrels in the white, and finish them out them selves, either with parkerizing, paint, or some other method. In all honestly unless your dead set you don't want a stainless barrel, your better off getting on in stainless. Buy the time you finish out the chrome moly barrel your at the same price point.