We show that the extraordinary crystal structure of TlAgTe results in a phonon-glass electron-crystal behavior. The material’s electronic transport properties are evaluated by first-principles calculations and Boltzmann transport theory. We find a multivalley conduction band (n-doping) and low dispersion at the valence band edge (p-doping), which results in a high power factor. Since the mean free path of a large number of phonon modes is found to fall below the Ioffe–Regel limit, semiclassical Boltzmann transport theory cannot describe the phonon transport, but a two-channel model must be applied. The lattice thermal conductivity turns out to be as low as 0.43 W m–1 K–1 because of strong lattice anharmonicity (originating from Tl 6s2 lone pairs) and low group velocities (originating from loose bonding of the Tl atoms), which renders TlAgTe to be a highly promising thermoelectric material.