If you do not have a license to carry concealed you may not carry a firearm openly or concealed. However, if you have a license to carry concealed you may carry your firearm on your person. Alternatively, you may store the firearm in a locked compartment, according to the new law's version of Ohio Revised Code 2923.16 (E) and (E)1:

(E) No person who has been issued a license or temporary emergency license to carry a concealed handgun under section 2923.125 or 2923.1213 of the Revised Code shall do any of the following:

(1) Knowingly transport or have a loaded handgun in a motor vehicle unless one of the following applies:

(a) The loaded handgun is in a holster on the person's person.

(b) The loaded handgun is in a closed case, bag, box, or other container that is in plain sight and that has a lid, a cover, or a closing mechanism with a zipper, snap, or buckle, which lid, cover, or closing mechanism must be opened for a person to gain access to the handgun.

(c) The loaded handgun is securely encased by being stored in a closed, locked glove compartment or in a case that is locked.

When the law was drafted, changes were made to 2923.16 which appear to make it illegal for a non-licensee to transport a handgun in a motor vehicle in any manner. This is a real problem that the legislature needs to remedy as it appears it is even illegal for a non-licensee to take a handgun to the range or even to take the range portion of the mandatory training.