I do not practice in OH, but I agree with the first answer: What do you mean by CCW? In WI, CCW = Carrying a Concealed Weapon. If that is what you are referring to, then yes: A DUI from 3 years ago would have no bearing on a CCW charge now. You could get a CCW.
If this is not the answer you are looking for, I suggest you repost and clarify your question.