Enantioselective alternating copolymerization of carbon monoxide with propylene, 1-heptene, 1-octene, and styrene was carried out using a palladium catalyst modified by 1,4-3,6-dianhydro-2,5-dideoxy-2,5-bis(diphenylphosphino)-L-iditol (DDPPI). The chiral diphosphine was proved to be effective for enantioselective copolymerization. The pure poly(1,4-ketone)s were obtained by dissolving the copolymers containing spiroketal and 1,4-ketone units in 1,1,1,3,3,3-hexafluoro-2-propanol and reprecipitating with methanol. Optical rotation, elemental analysis, and H-1 NMR, C-13 NMR, and IR spectra showed that our copolymers were optically active, isotactic, alternating poly(1,4-ketone) structures. An oxidant and a weakly or noncoordinating anion were important in the copolymerization.