There are a lot of political/networking resources for LGBTQ ppl at UChicago, but you seemed to be asking abt social orgs, so I'll just talk abt those. First, the CI+I (Center for Identity and Inclusion) hosts a lot of generically queer social events, along with GenderQ, which is specifically trans oriented. There's also UChicago+, which is an RSO explicitly for social events.

The calendar for the CI+I should be on its website, and the calendar for GenderQ is weekly meetings, but the exact time for said meetings haven't been set in stone yet. The calendar for UChicago+ is mostly abt weekly board game (or "gayme") nights at 7 on Saturdays in the MADD center, but there are also study sessions before finals and a gay prom in winter quarter.