Yes. It is a constitutionally protected right in Ohio. See Klein v. Leis, 99 Ohio St.3d 537.
I have received a couple calls on this issue so I wanted to put this here to clarify. In Ohio, you may open carry. Now, there are some restrictions as usual such as you cannot open carry and walk into a bar. You also cannot open carry and enter a federal building. Even CCW permit holders must leave their firearms in their vehicles when entering a federal building.
As always, when in doubt, it is better to ask than to take a chance.