I'm sure my neighborhood isn't zoned for chickens either but a neighbor behind me had one that would sit on top of the fence and cluck all day.

The neighbor next to me would feed it...dang chicken was smart. When it wanted to eat, it would peck at her side door.

No one cared about a chicken being dirty, it was entertaining. (of course it never pooped on my fence)
Although, had that been a rooster, there may have been some issues with the neighbors at dawn : )