I won't avoid it.
In the past decade, between my family and I, we have been to Belfast, Bosnia, New Orleans, Ciudad Juarez, Guatemala City, Pine Ridge, Guadalajara, and yes, Chicago. Aside from a little credit card issue, our only incident involving crime was being pick-pocketed in Rome.
Keep your head on a swivel, know where you are going and treat everyone you meet with courtesy and a caution. Life is too short to be afraid of shadows.