New materials have been playing a continuously more important role in advancing thermoelectric technology. Many known novel thermoelectric materials share the similarity of an intrinsic low lattice thermal conductivity (κ L ) due to various mechanisms. Because heat is generally conducted by acoustic phonons because of the much higher velocities as compared to those of optical phonons, many known low-κ L thermoelectrics rely on the complexity of crystal structure to lead the fraction of acoustic phonons to be small. In addition to structural complexity, an overall low sound velocity is found to be helpful for realizing an extremely low κ L . In this work, a new thermoelectric compound Ag 5−δ Te 3 , having both a complex crystal structure and a low sound velocity (∼1300 m/s), is shown to be one of the least thermally conductive dense solids (κκ L ∼ 0.2 W/ m•K). The resultant high thermoelectric figure of merit, zT, of unity, with the help of its large band gap of ∼0.6 eV, leads this material to be superior to known silver tellurides. These preliminary results demonstrate Ag 5−δ Te 3 as a promising thermoelectric material, with possibilities for further improvements particularly through enhancements focusing on electronic properties.