First, I live in town and a rooster crowing between the hours of 10:00pm and 8:00am - I would put in the same class as dogs barking, not something a good neighbor would allow.
However , Chicago and its inhabitants might be better served by an ordinance that caters to
all the people. They could disallow roosters (or better yet put a continuous noise clause in their ordinance), and limit the hens by the area of the property, so many square feet per bird.
The truth of the matter is that the main reason that people want to get rid of chickens is appearance. They are dignified (picture nose up in the air sort ) . I use to go to Chicago on business and the people over all always struck me as good folks, things might work out all right yet.