A few thoughts on this.

First, if you're relatively close to the gig, it would be possible to have a backpack guitar case and pedal there. I do this when I'm playing guitar at church. It's quite a simple solution, but I've got an acoustic guitar, so it's not a big deal for me. If I needed to bring an amp as well, chances are good I'd get a trailer for that.

Second, if you and your bandmates have to haul drums, guitars, amps and more, or if you have gigs that are more than around 10 or 15 kilometres from where you live, it would be worthwhile to carpool. If the band looks like it will stay together for some time and if you all trust each other, you might even pool your money and get a used minivan as the band's transportation unit. This solution puts you squarely in the car-light, not car-free category. It's a compromise. (The reason I use 10 to 15 kilometres as the cutoff is because of the time spent cycling. After a concert, when it's dark and you're riding home, you might not want to be on a long ride, especially on a weekend when tipsy motorists are heading home after last call.)

Third, along the same lines, if you and your bandmates were to take a taxi, it might be a possibility. Check the rates first.

Fourth, since you're in the Chicago area, public transportation may be a possibility. This depends to a great degree on how much you have to haul and how the transit routes and schedules will work for you. In cities where I've lived, transit schedules are great for getting people out to the night spots, but not so good after everything had closed. Chicago is a much larger city so it may have a better night service.