We examine the thermodynamics of phase separation and ordering in the ternary CaxPb1-xS and SrxPb1-xS systems by density-functional theory combined with a cluster expansion and Monte Carlo simulations. Similar to most other ternary III- V or IV-VI semiconductor alloys, we find that bulk phase separation is thermodynamically preferred for PbS-CaS. However, we predict the surprising existence of stable, ordered ternary compounds in the PbS-SrS system. These phases are previously unreported ordered rocksalt-based compounds: SrPb3S4, SrPbS2, and Sr3PbS4. The stability of these predicted ordered phases is confirmed by transmission electron microscopy observations and band gap measurements. We believe this work paves the way for a combined theory-experiment approach to decipher complex phase relations in multicomponent chalcogenide systems.