I have a solution to the problem; some of those being shot are just innocent bystanders (that day anyways):

Take one of the run down vacant concrete and masonry buildings on the south side and invite the public to use it to settle disputes with courage and honor. Run ads on local TV; the slogan could be "Two men walk in, One man walks out". No spectators allowed, this is for safety after all (not entertainment). Have the press report any shooting done outside of the building as a "shooting by a coward".

It will need to be supervised (keep in line, wait your turn!) and a reservation system might be needed for holiday weekends (usually very busy time for shootings in Chicago), but I am thinking the police can handle the staffing (they could also cross off the dead as suspects in ongoing cases). The place could be sponsored by an ammo company or a gun manufactured ("Remington Thunder Dome" or "Glock Coliseum"). The guys who sign up as organ donors (the police could have the forms on hand) would be provided with a free cremation if they lost.

I believe the real key to success is changing the way these shootings are portrayed in the press; all of these clowns want respect, none of them want to be known as cowards.