I have a trip coming up to Chicago in early December and would appreciate any recommendations - my interest runs mainly to bolt-action Winchesters, Mausers and custom rifles built on those actions. Many thanks

Chicago Gunshops? Isn't that an oxymoron? Plenty of street weapons though I doubt they are what you are looking for.

When you get there look for anyone wearing lots of red or blue clothing. These guy's will know.

GAT Guns in Dundee would be worth looking at.
They have a website and are about 40 miles from Chicago.
Other than that, Cabelas has a store in Hoffman Estates that's about midway between the two.

Up north is Smoke N' Gun in Waukegan, I'd suggest calling them and seeing what they have in inventory.