We provide a comprehensive theoretical assessment at the level of density functional theory (DFT) of the stability of various coinage metal–sulfur complexes, both in the gas phase and also for the complexes adsorbed on the (111) surface of the same coinage metal. Our primary interest lies in the latter where earlier scanning tunneling microscopy (STM) experiments were interpreted to suggest the existence of adsorbed S-decorated metal trimers, sometimes as a component of more complex adlayer structures. Recent STM studies at 5 K directly observed other isolated adsorbed metal–sulfur complexes. For these adsorbed species, we calculate various aspects of their energetics including a natural measure of stability corresponding to their formation energy from sulfur adsorbed on terraces and from metal atoms that are in thermal equilibrium with the substrate. From this perspective, our DFT analysis shows that all of Ag2S3, Ag3S3, and many larger complexes on Ag(111) are strongly stable, Cu2S3 is stable, and some larger complexes are marginally stable on Cu(111), but only Au4S4 on Au(111) is stable. Results are consistent with STM observations for Cu(111) and Ag(111) surfaces but appear to deviate slightly for Au(111). A systematic analysis relating stability in the gas phase with that of adsorbed species is achieved within the framework of Hess’s law. This analysis also unambiguously elucidates various energetic contributions to stability.