http://www.amlegal.com/nxt/gateway.dll/Ohio/englewood_oh/cityofenglewoodohiocodifiedordinances?f=templates$fn=default.htm$3.0$vid=amlegal:englewood_oh
The above is a link to the city zoning regs. All I could find specifically mentioning poultry was this:
(m) No livestock or poultry, quartered or housed within the corporate limits, shall be kept and maintained so as to produce objectionable noise, odor, destruction of property or health problems.
I did a search for agriculture and other than saying you have to keep the housing clean and odor free poultry does not appear to be prohibited:
(a) No person shall erect, continue to use, or maintain a building, structure, or place for the exercise of a trade, employment, or business or for keeping or feeding an animal which, by occasioning noxious exhalations or noisome or offensive smells, becomes injurious to the health, comfort, or property of individuals or of the public.
(b) No person shall cause or allow offal, filth, or noisome substances to be collected or remain in any place to the damage or prejudice of others or of the public.
Agriculture. "Agriculture" means the use of land, buildings or structures for nurseries, greenhouses, farming, dairying, pasturage, apiculture, horticulture, floriculture, viticulture and animal and poultry husbandry.
If you have more than 5 acres and are outside city limits you are exempt from (a) and (b).
I think you might be able to have a few chickens.