Chicago is no worse, and probably a lot better than most other large cities. The vast majority of shootings are people that live in the ghettos and deal drugs. West and particularly and SW sides.
As somebody who actually lives in Illinois, unlike most of the folks responding, and lives in a suburb five minutes from the city, oh and goes into the city on a daily basis......I'd say don't worry about the gun and have to agree with the person I quoted. Your staying downtown right, most likely you are so you have little to worry about as most of the crime happens in the surrounding sprawl of the city(particularly the south side) so unless your doing business there I'd say just relax and enjoy seeing the sights.
The REAL danger is the parking in the loop, heck pricing there will cost you an arm and a leg.