  The development of efficient thermal energy management devices such as
thermoelectrics, barrier coatings, and thermal data-storage disks often relies
on compounds that possess very low lattice thermal conductivity ($\kappa_l$).
Here, we present the computational prediction of a large family of 628
thermodynamically stable quaternary chalcogenides, AMM'Q$_3$ (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 low-$\kappa_l$ in this family
of materials by calculating $\kappa_l$ of several predicted stable compounds
using the Peierls-Boltzmann transport equation within a first-principles DFT
framework. Our analysis reveals that the low-$\kappa_l$ in the AMM'Q$_3$
compounds originates from the presence of either a strong lattice anharmonicity
that enhances the phonon scatterings or rattlers cations that lead to multiple
scattering channels in their crystal structures. Our predictions suggest new
experimental research opportunities in the synthesis and characterization of
these stable, low-$\kappa_l$ compounds.
