A quantitative ab initio study of the carbon isotope-exchange reaction 13C12CS + H → 12C13CS + H was performed at the RCCSD(T)/aug-cc-pVQZ//M06–2X/aug-cc-pVTZ level of theory, revealing that this reaction is barrier-less. This result validates the chemical hypothesis of Furuya et al., who suggested this reaction to be responsible for the 12C13CS/13C12CS isotopomer ratio observed to be higher than unity in cold interstellar clouds.