I have to disagree, it is all based off of the cities ordinances. When we lived in Vegas I was wanting to get an exotic pet. Vegas has no law other then the fact you have to have them in a safe environment so that they cant get out or hurt people.. Any Joe blow could own a tiger in Vegas if they had the land or the proper cage for said animal.
yes. You can own a zebra as a private owner if the local ordances allow it. Its legal in states like Ohio, Georgia, Florida (parts of the state) and Missouri.
All that said, I DO NOT recommend zebras as pets. I've heard stories of halter broke zebras, but I've never seen one, and to be honest, I seriously question just how healthy those animals are.