Hi Mike
The LDS family history library has films that cover County marriages in Illinois for the time period you are seeking.
It appears you would need to order first the index, then another film to view the marriage license.
I looked under Place Search, enter, Cook, part of Illinois, then down to Vital Records.
Hope there is a FHC near you. This would be cheaper in the long run, as marriage certs are $15 from IL.
Regards
Valerie