This may sound callous, I don't think this or the new CC law will make much of a difference. As has been said in this post, red tape will be crazy and long for a CWP.
Most people there are probably conditioned to not see a CCW as a solution to the crime and murder. These people for the most part probably don't know any different from the "Sh!tcago Way".
Then to top it off, cops aren't in favor of CCW in Chicago and have said that it will cause lots of problems and they will shoot people with a gun. I'm pretty sure someone posted that "Halt Or I'll Shoot" article here about the LEO hostility towards CC in Chicago.