We investigate theoretically the ternary copper chalcogenides with the general formula Cu 2 M II M IV S 4 . This family of compounds can crystallize in two different non-centrosymmetric structures, I42m or Pnm2 1 . We show that all the reported members of Cu 2 M II M IV S 4 having the Pnm2 1 symmetry exhibit a large spontaneous polarization. This result suggests that several of these materials are likely to be multiferroics since they order magnetically at low temperature. We discuss in detail in the framework of Landau theory the members Cu 2 MnSnS 4 and Cu 2 MnGeS 4 which should present both a linear magnetoelectric effect and multiferroic behavior.