Under our G2G Integrators project, I've started a profile for Alice. Pamela, please message me with your email address, and I'll make you the manager :) I've added tags to this question to make it easier for potential helpers to find. The profile is open, so if anyone has sources or more information, please share it there, too!
The 1940 census says that she worked in the "check room" (coat check?) at a nightclub. A good place to look would be a 1940 city directory for Chicago to see what nightclubs, dance halls, and music venues were near her home and poke about doing some research on the general nightlife of Chicago to see what you may turn up.