Is it worth it to send my child to a Catholic school?

Unfortunately, I'm obligated/forced to live in the city of Chicago, which I am very disgusted with -- a filthy, over-populated hole in the ground overflowing with crime and corruption. With that in mind, sending my child to a Chicago Public School seems more of a risk; my child would encounter gang members at a higher rate! Pardon my frustration, but I'm in a dilemma! Yes, academic success very much depends on the mental limit or capacity of the child regardless of the school, but if it means having to work extra jobs to send my child to a Catholic school, then so be it. I appreciate any suggestions. Thank you...