Most (but not all) racing motorcycles use a chain-drive system. There are some exceptions, such as Moto Guzzis (which have had great success in the past) and BMWs, both of which are shaft-drive, for the most part. And Buells, which have a belt-drive, also are raced.
But the premier racing leagues are dominated by chain-drive motorcycles, primarily because of the weight savings and ease of adjustability. Weight is even more important on a machine in which the power is human supplied, at least if you want to ride fast.