Chalcogenide perovskites (CPs) have recently attracted interest as a class of materials with practical potential in optoelectronics and have been suggested as a more thermally stable alternative to intensely studied halide perovskites (HPs). Here we report a comparative study of the thermal stability of representative HPs, MAPbI3 (MA = CH3NH3+, methylammonium) and CsPbI3, and a series of CPs with compositions BaZrS3, β-SrZrS3, BaHfS3, SrHfS3. Changes in the crystal structure, chemical composition, and optical properties upon heating in air up to 800 °C were studied using thermogravimetric analysis, temperature-dependent X-ray diffraction, energy-dispersive X-ray spectroscopy, and diffuse reflectance spectroscopy. While HPs undergo phase transitions and thermally decompose at temperatures below 300 °C, the CPs show no changes in crystal phase or composition when heated up to at least 450 °C. At 500 °C CPs oxidize on time scales of several hours, forming oxides and sulfates. The structural origins of the higher thermal and phase stability of the CPs are discussed.