I am pretty sure it is original to the house which was built in 1987, It has a acrylic knob that you push up to turn on, then twist to get it to hot or cold.
My first view of the stem made me think chicago faucet do to the tapered square stem. but had never seen a shower cartridge. Delta was my quick guess but I did some research and I found it chicago faucet makes a few shower valves this beeing one of their pressure ballance units. Chicago Faucets - 1900-006KJKNF Pressure Balancing Valve Rebuild Kit
That's not Delta. Delta never had screws holding the cartridge in. But it looks like your right on with it being Chicago. That I have to say is one faucet that I have no experience with. We just keep learning every day. Good job zkirtlink.