Oklahoma does not have a state law that permits or bans backyard chickens. The decision sits entirely with individual cities, which means the rules change completely depending on which side of a city line your property falls on.
The general pattern
Most of Oklahoma's larger cities allow hens in some form, almost always ban roosters outright due to noise, and require some kind of setback between the coop and neighboring homes. A handful require a paid permit, others don't. A few cities, including at least one major metro suburb, have specifically studied and rejected chicken ordinances, so it is not safe to assume a nearby city's rules apply to yours.
Why HOAs matter as much as city code
A city ordinance allowing chickens does not override a homeowners association covenant banning them. Both layers apply, and the stricter one wins. If your property sits in an HOA, check the covenant before you check the city code.
How to check your specific city
Use the city finder on the homepage or browse the full city list to find your ordinance summary, permit requirements, and setback distances. Every city page links to the actual municipal code where one is available, and notes when an ordinance has changed recently or is currently being reconsidered by a city council.
Ordinances change without much public notice. Treat every city page here as a starting point for a call to your city hall or code enforcement office, not a final legal answer.