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The development of efficient thermal energy management devices such as thermoelectrics and barrier coatings often relies on compounds having low lattice thermal conductivity (κ_l). Here, we present the computational discovery of a large family of 628 thermodynamically stable quaternary chalcogenides, AMM′Q₃(A = alkali/alkaline earth/post-transition metals; M/M′ = transition metals, lanthanides; Q = chalcogens) using high-throughput density functional theory (DFT) calculations. We validate the presence of lowκ_lin these materials by calculatingκ_lof several predicted stable compounds using the Peierls–Boltzmann transport equation. Our analysis reveals that the lowκ_loriginates from the presence of either a strong lattice anharmonicity that enhances the phonon-scatterings or rattler cations that lead to multiple scattering channels in their crystal structures. Our thermoelectric calculations indicate that some of the predicted semiconductors may possess high energy conversion efficiency with their figure-of-merits exceeding 1 near 600 K. Our predictions suggest experimental research opportunities in the synthesis and characterization of these stable, lowκ_lcompounds.