This is very familiar. Years ago, I and a group of folks wishing to raise chickens got together and placed this topic on the agenda with our city council. We all attended the meeting, with large amounts of supportive materials, and filed to address the council that evening. The council took a vote, and approved backyard chickens. That being said, none of us were in subdivisions with HOAs. If you have an HOA, then you'll have to address that board, too.
Some folks decide to go ahead with a few hens despite ordinances. That's risky, IMO. If neighbors are all agreeable, you might get away with it. If someone complains, it will be an issue.