Even though I've gotten several custom stainless barrels, I've never ordered
a chrome-molly barrel prior to the one just received. To compare, I looked
into the chambers of a couple factory rifles and it appears the chambers were
blued at the factory. That brings up the question, should I blue the chamber
and chamber neck?

You asking about a blued chamber on a CM barrel? If so when it is hot blued the barrel is open so the ID gets blued the same time as the OD. On a rust blue I don't "think" they blue the ID.

With rust blue,most would leave the ID alone, in fact avoid any contact. I coat ID with a thin coat of varnish. I'm sure most try to protect the bore in some manner

I don't protect the chamber or bore whilst rust bluing;
it won't rust, like you think it would. I use the steam method though.
You do want to avoid any application of the acid to either the muzzle bore, or the chamber. That would be a bad thing. Of course, salt bluing does blue the bore and chamber; yes that is a microscopic etch, but it doesn't matter.

OK, thanks guys!