To briefly reply to Expat - IMO Chicago is a phenomenal city and should not be avoided. For the majority of people, especially tourists, you won’t encounter crime. Like any large city, it has significant issues concentrated mainly in specific deprived neighbourhoods. But having lived there for 10 years, I cannot recommend it highly enough.
Back on topic though - I believe simple measures such as mandatory background checks, waiting periods and eliminating gun show loopholes would go some way to helping the problem. It certainly would not eliminate the problem, but it would be a start before tackling the issue of large capacity, semi-automatic weapons.
Sadly, given the current imbalance of the supposed “co-equal branches of government”, I don’t think anything significant will be done anytime soon.