Accelerating the discovery of new materials is crucial for realizing the vision of need-driven materials development. In the present study we employ an integrated computational and experimental approach to search for new thermoelectric materials. High-throughput first principles calculations of thermoelectric transport coefficients are used to screen sulfide compounds conforming to the boundary conditions of abundant and innocuous components. A further computational screening step of substitutional defects is introduced, whereby SnS doped with monovalent cations is identified as having favorable transport properties. By silver doping of SnS under S-rich conditions an electric conductivity more than an order of magnitude higher than reported previously is realized. The obtained thermoelectric power-factor at room temperature is comparable to the state of the art for thermoelectric materials based on earth abundant, non-toxic elements. The high-throughput screening of extrinsic defects solves a long standing bottleneck in search of new thermoelectric materials. We show how the intrinsic carrier concentration in the low-temperature phase of SnSe is two orders of magnitude higher than in SnS. We furthermore find that the carrier concentration in SnSe can still be further optimized by silver doping.