Christian romantically involved with a Non-Christian

Is it okay to be romantically involved with a guy who doesn't share my Christian faith? He asked me out on a date six months ago, and though at the time I didn't think it was a good idea, I went ahead and accepted. Now he's captured my heart and I don't know what to do. I'm in pretty deep, but unless he makes a commitment to follow Jesus I don't think I can marry him. At the same time, if there's a chance that he may accept Christ, I don't want to break things off and throw away the most wonderful relationship I've ever experienced. What should I do?