We investigate theoretically the ternary copper chalcogenides with the general formula Cu2MIIMIVS4. This family of compounds can crystallize in two different non-centrosymmetric structures, I ¯42m or Pnm21. We show that all the reported members of Cu2MIIMIVS4 having the Pnm21 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 Cu2MnSnS4 and Cu2MnGeS4 which should present both a linear magnetoelectric effect and multiferroic behavior.