I do not know about Chicago, but I knew friends at California: the couple went to fish w/o license and were caught by two cops--a rookie and veteran one. It seemed that the veteran one tried to find a case for the rookie one to learn how to write a ticket, it took about one hour for the rookie one to finish the ticket, during that time the couple were so afraid--they wondered why it took so long, was it a serious offense? would it affect Greed Card application? Apparently the veteran cop noticed the frighten shaken couple's pale faces, he told them it was a minor offense, no big deal.
The couple got the GC w/o any problem.
Do not worry.