The Mizoroki–Heck polymerization of cinchona-based sulfonamide dimers and aromatic diiodides was investigated in the presence of a palladium catalyst, to obtain chiral polymers in high yields. An iodobenzenesulfonamide derivative of a cinchona alkaloid was also polymerized via self-polycondensation under the same reaction conditions. The catalytic activities of these chiral polymers were examined by using them as catalysts in the enantioselective desymmetrization of cyclic anhydrides.