Asymmetric alternating copolymerization of CO2 and cyclohexene oxide (CHO) proceeds effectively under mild temperature and pressure for yielding isotactic-enriched poly(cyclohexene carbonate) ( PCHC) with a narrow molecular distribution, by using a binary catalyst system of a chiral tetradentate Schiff-base cobalt complex (SalenCoX) in conjunction with a bulky ionic organic ammonium salt such as bis(triphenylphosphine) iminium chloride (PPNCl). An increase in the temperature between 25 and 80 C results in a dramatic increase in activity and a slight decrease in enantioselectivty, but the variation of temperature does not lead to an observable decrease in selectivity for PCHC formation. The binary catalyst system is also very effective in the terpolymerization of CO2 with CHO and propylene oxide (PO) to selectively provide polycarbonates with a narrow polydispersity (Mw/Mn ratio) of 1.24 and > 99% carbonate linkages. The resulting terpolymer has only one glass transition temperature (Tg) and one thermolysis peak. The unprecedented results are tentatively assumed that an alternating nature of the two different carbonate units predominantly exists in the resulting polycarbonate. Furthermore, the Tg of the PO/CHO/CO2 terpolymer can be easily adjusted by controlling the proportion of cyclohexene carbonate linkages and propylene carbonate linkages.