Properties of solids are strongly influenced by their crystal structures. Learning from the structure–property relationships of existing high-performance thermoelectrics (TEs), here we identify a family of quaternary chalcogenides AMM′Q3 (A= alkali, alkaline earth, post-transition metals, M/M′ = transition metals, rare earth, actinide elements, Q = chalcogens), which are expected to exhibit promising TE performance. They possess Am+ cations, which are weakly bonded to the lattice and are sandwiched between the strongly bonded [MM′Q3]m− layers. Using first-principles density functional theory (DFT) calculations and taking two representative compounds (TlCuZrSe3 and BaCuYTe3) from a large family of known semiconductors, we show how localized phonon modes arising from the rattling-like Am+ cations induce low lattice thermal conductivity, whereas the delocalized charge density within the [MM′Q3]m− layers leads to an enhanced thermoelectric power factor. A combination of these two factors give rise to a promising thermoelectric figure of merit (zT), a metric that quantifies the energy conversion efficiency of TEs. In addition to the structural degree of freedom, our work also demonstrates how valence m associated with Am+ and [MM′Q3]m− layers influences the lattice distortion, electronic structure, phonon dispersion, electrical, as well as the lattice thermal transport properties of these compounds. We hope this work will encourage experimental investigations of the structure-valence-property relationships in this largely unexplored class of quaternary semiconductors, which are predicted to be potential thermoelectrics.