Single crystalline SnSe has been reported to exhibit the high thermoelectric zT value of 2.6 at 923 K along the b-axis direction, due to its low thermal conductivity [Zhao, L. D.; et al. Nature 2014, 508, 373]. However, the strongly anisotropic properties of the orthorhombic structure degrade the thermoelectric performance of polycrystalline SnSe, resulting in a low zT of 0.6 and 0.8 for Ag- and Na-doped SnSe, respectively. Here, we prepared Ag_0.01Sn_0.99Se_1–xS_x (x = 0, 0.10, 0.15, 0.20, and 0.35) compounds by melting and hot press sintering. The compounds showed extremely low thermal conductivity (0.11 W m^–1 K^–1 at 825 K for x = 0.15). Using transmission electron microscopy images, we found that SnS alloying induced numerous nanoscale point defects. A Debye–Callaway model analysis supported the conclusion that the extremely low lattice thermal conductivity could be attributed to the point defect scattering of phonons. This resulted in a high zT of 1.67 at 823 K for the x = 0.15 sample, which is the state-of-the-art zT value for polycrystalline SnSe. Because the compounds are based on the environmentally friendly and cheap materials Sn, Se, and S, they make promising candidates for thermoelectric applications.