The Chevrel phase (CP) is a class of molybdenum chalcogenides that exhibit compelling properties for next-generation battery materials, electrocatalysts, and other energy applications. Despite their promise, CPs are underexplored, with only ∼100 compounds synthesized to date due to the challenge of identifying synthesizable phases. We present an interpretable machine-learned descriptor (Hδ) that rapidly and accurately estimates decomposition enthalpy (ΔHd) to assess CP stability. To develop Hδ, we first used density functional theory to compute ΔHd for 438 CP compositions. We then generated >560 000 descriptors with the new machine learning method SIFT, which provides an easy-to-use approach for developing accurate and interpretable chemical models. From a set of >200 000 compositions, we identified 48 501 CPs that Hδ predicts are synthesizable based on the criterion that ΔHd < 65 meV/atom, which was obtained as a statistical boundary from 67 experimentally synthesized CPs. The set of candidate CPs includes 2307 CP tellurides, an underexplored CP subset with a predicted preference for channel site occupation by cation intercalants that is rare among CPs. We successfully synthesized five of five novel CP tellurides attempted from this set and confirmed their preference for channel site occupation. Our joint computational and experimental approach for developing and validating screening tools that enable the rapid identification of synthesizable materials within a sparse class is likely transferable to other materials families to accelerate their discovery.