The mechanism of the Cu + CS2 reaction has been investigated using density functional and coupled cluster calculations. The lowest energy route on the potential energy surface corresponds to the insertion product SCuCS via the formation of intermediate coordination complexes: eta(S)(1) and eta(CS)(2), which all lie below the energy of the reactants. Another path corresponding to the formation of a cyclic C-2nu compound eta(SS)(2) leads to the same insertion product, but it involves a higher energy barrier (34.7 kcal/mol vs 26.9 kcal/mol with respect to the reactants at the CCSD(T) level). The dissociation of the insertion product SCuCS into the CuS and CS fragments is found to be endothermic by 43 kcal/mol (CCSD(T) level). Our results are related to experimental data obtained in low-temperature rare gas matrixes and in the gas phase.