Enantioselective, alternating copolymerizations of carbon monoxide with styrene, dicyclopentadiene, and methylcyclopentadiene dimer were carried out with a palladium catalyst modified by 1,4-3,6-dianhydro-2,5-dideoxy-2,5-bis(diphenyl phosphino)-L-iditol. Chiral diphosphine was proven to be effective at enantioselective copolymerization. In the copolymers, some of the second double bonds of alternating poly(1,4-ketone) were carbonylated. Optical rotation, elemental analysis, and spectra of H-1 NMR, C-13 NMR, and IR showed that the copolymers had isotactic, alternating poly(1,4-ketone) structures. An oxidant and an organic acid were the promoters of the copolymerization.