Synthesis of chiral sulfur‐containing polymers was realized for the first time by the asymmetric alternating copolymerization of achiral meso‐epoxides with carbonyl sulfide (COS) using catalyst systems based on enantiopure binaphthol‐linked dinuclear CoIII complexes under mild reaction conditions. The resultant poly(monothiocarbonate)s have main‐chain chirality and more than 99 % isotacticity. Notably, the stereoregular copolymers are typical semicrystalline thermoplastics with high melting temperatures up to 232 °C. Additionally, these sulfur‐containing polymers have good optical properties with refractive indices of up to 1.56 and Abbe's numbers of up to 43.