Without being a CHL holder, you have to go by the long established Ohio transport laws. In short, the firearm and ammo must be seperate from each other, for example the pistol locked in the trunk, ammo in the passenger compartment, or vice versa. (Been my experience that most Ohio LEOs would be satisfied if you had both gun and ammo in the trunk and away from each other, also.) Obviously if you're driving a pick up, van, etc., you have to make that same best-faith effort to keep the firearm and its ammo apart. To comply with the "spirit"/working definition of the law,according to prosecutors and judges, is a 'no' answer to the following hypothetical question: "Could thedriver (and passenmgers) of the vehicle have accessed the loaded firearm without first stopping the vehicle and getting out?" The ORC lists off a few otherexample of ways to legally transportfirearms, most of that language would be more applicable to long guns.
Be warned however, that when Ohio's CHL law was passed, some of this language was removed, apparently in error. A quick, literalreading of these poorly revised sections of the ORC now would lead one to believe that there is no longer a legal way for non-CHL holders to transport even unloaded firearms. But it is my strong suspicion that this was just a boneheaded oversight, and only the most malicious of police or prosecutors would make any attempt to exploit this against someone who was truly making a best-faith effort to comply.