I work shift work. Have been working shift work for 31 years, the number of times I have been awaken in the middle of my day of sleeping is unnumberable. Hundreds of times, lawnmowers, salesman, loud cars, motorcycles you name it. For what it's warth I take all these disturbances with a graine of salt, most of the rest of the world is on a daylight to dark schedule, I can't hold them responsible for my sleep requirements. Most noise laws pertain to times in the evening hours.
For instance: You/I, live next to a empty lot, some one buys it and decides to build a home. Are the caprenters not aloud to work during the day because you or I work night shifts?
Nieghbors and chickens:
In the situation the OP is describing, evidently a very closely built urban setting. Quiet professional nieghborhood. With out a doubt I can garauntee, even if those chickens were completely and totally silent, one of the nosey rosey nieghbors will have something negative to say. Some people can't stand to see their nieghbors enjoy life.
It may have been discussed earlier, do you have any laws, bylaws, or covenants applying to the housing of chickens? Are they being adhered to? If so, mind your own business and enjoy your chickens.
I have recently, discovered that my long term nieghbors will be moving. They have been the best nieghbors anyone could ever have. An elderly couple in their 80s now, been there for 20 years. Even though my children had grand parents, this old couple became a "third set" of grand parents to my children. Welcomed my dog, into their home. Were invited to all family functions. Now they are moving to be close to family. Kind of made me feel bad, like saying to me I haven't been good family to them. By the way these are the only nieghbors we have within rifle shot. Going to be some new folks moving in soon, I bet it's gonna get interesting with my chickens and roosters. My wife says, the nieghbors are not buying the scenery, and no laws against chickens. Me I'm waiting to see, praying that we get another good set of nieghbors.