...111 links to compensate for the extra tooth or can I get away with a stock 110 links if I only add 1 tooth?
You probably do not need to buy another chain just for a one tooth difference. Just put the sprocket on move the rear wheel all the way forward and you will have your answer.
I agree that the stock chain may work fine. One tooth is just a half tooth as far as chain length goes. The chain only goes about half way around. Also you wouldn't want e a 111 link chain. You would have to use an offset master link The next length increase is 112.