The reaction of MnTe with AgSbTe2 in an equimolar ratio (ATMS) provides a new semiconductor, AgMnSbTe3. AgMnSbTe3 crystallizes in an average rock-salt NaCl structure with Ag, Mn, and Sb cations statistically occupying the Na sites. AgMnSbTe3 is a p-type semiconductor with a narrow optical band gap of ∼0.36 eV. A pair distribution function analysis indicates that local distortions are associated with the location of the Ag atoms in the lattice. Density functional theory calculations suggest a specific electronic band structure with multi-peak valence band maxima prone to energy convergence. In addition, Ag2Te nanograins precipitate at grain boundaries of AgMnSbTe3. The energy offset of the valence band edge between AgMnSbTe3 and Ag2Te is ∼0.05 eV, which implies that Ag2Te precipitates exhibit a negligible effect on the hole transmission. As a result, ATMS exhibits a high power factor of ∼12.2 μW cm-1 K-2 at 823 K, ultralow lattice thermal conductivity of ∼0.34 W m-1 K-1 (823 K), high peak ZT of ∼1.46 at 823 K, and high average ZT of ∼0.87 in the temperature range of 400-823 K.