Open carry is legal in Ohio but with a couple caveats.
1. Carry in a motor vehicle is considered concealed whether the handgun is visible or concealed. Thus a concealed handgun license is required to be legal.
2. Carry in an establishment serving alcohol is legal with a CHL but illegal without a CHL. An open carrier has to be careful about grocery stores because if the store has a wine tasting in the back of the store, you would be committing a crime and not even know it.