The "ghost manufacturers", such as Gardner-Wells and Continental, in addition to building a gigantic number of sets for the national chain stores like Wards and Sears, also were happy to create small production runs of "private label" sets for local or regional retail store chains. These were usually existing radio designs that simply were re-badged (new dial artwork and/or case stickers/decals)for the new, small-volume customer. This minimized "non-recurring" (design engineering and tooling) costs and kept the sell price reasonable. I suspect that your set is one of this type. It may say "Chicago" on it, but that was probably just where it was made. It could have been shipped to, and sold, almost anywhere in the continental US.
You might try posting clear front and rear photos of your set. If it is a "private label" radio, there is a high probability that someone will recognize it in a more familiar brand incarnation.
Richard