I'm in a place with no specific ordinances about chickens too. And I'm right in the heart of such downtown as a town this small actually has.
Per the mayor's husband they had been forbidding chickens based on the no-farming ordinance -- until someone pointed out that the same logic would require forbidding people's home gardens.
The unwritten policy is that if your neighbors don't complain you're OK. If they do complain any complaints will be evaluated based on noise and sanitation ordinances and unreasonable complaints will not get very far.
It pretty much works out to no roosters, keep it clean, do any slaughtering discreetly rather than in full, public view, keep the chickens in your own yard, and don't sell any eggs or other chicken products. The town is far more concerned about people letting dogs run loose than about properly-kept, backyard chickens.