I'm sorry to say, he is probably a selfish asshole and you just aren't seeing it. But to give him the benefit of the doubt, write down the $ that it takes to live, and be sure to include everything from the electric bill down to milk and toilet paper. Tell him you both need to put a certain amount every month into a jar to cover those expenses. It could be equal, or (more fairly) it could be a percentage of both your incomes. If he responds badly, you have your answer. (And if he responds well, the problem is solved.) Here's another red flag - whose name are the bills in? Put the rent and electric bills in his name, and make him hound you for the money.
Chores are a little harder, because if he was living alone, he might not really be doing as much cleaning and stuff as you are doing. Can you slack off on those things and still stand to live there? Then if it bothers him, he'll start doing more.
If he does respond well to splitting the finances, then you can bring up splitting the chores more fairly a couple weeks down the road.