I and about four other individuals petitioned our city council regarding chickens about ten years ago, and prevailed. The first thing we did was garner as much research on the benefits of permitting chickens on residential lots, and as much sound information for dispelling myths about keeping chickens. We focused on the fact that there were current codes in place to regulate noise and odor (for other pets/animals) that would be applicable to chickens. Ultimately, after a number of us spoke at a meeting, the vote was called for incorporating chickens into the municipal codes. The vote passed!
Every city or town has different forums for presenting information. Ours requires a speaker to attend a meeting and fill out a request to speak - pretty simple. The internet is full of good information, as is this site, supporting keeping chickens.
1) eggs
2) compost
3) ability to show for FFA/Ag (school-aged kids)
4) weed control
In residential areas, if chicken pens and coops are kept scooped and clean, there are no more issues with odor than any other animals. In fact, outdoor cats pose more of a health risk via parasites/illness (toxoplasmosis) due to their ability to roam onto other properties. Proper food and water storage also eliminates rodent incentives (just as with outdoor dogs). Hens do make a bit of noise from time to time, but no more than barking dogs. (We actually found a decibel study regarding animal noise to support.)
Good luck!!