Your gun must be transported according to Ohio law (2923.16). An unloaded gun must be transported in one of the following ways:
(1) In a closed package, box, or case;
(2) In a compartment that can be reached only by leaving the vehicle;
(3) In plain sight and secured in a rack or holder made for the purpose;
(4) In plain sight with the action open or the weapon stripped, or, if the firearm is of a type on which the action will not stay open or which cannot easily be stripped, in plain sight.

Also, if a CHL-holder's gun is going to be transported in the passenger compartment in any manner (one of the above) other than in a visible locked case, a locked glove compartment, or in a holster that is in plain sight on the person's person, any ammunition must be inaccessible from the driver or other passengers.