For efficient thermoelectric materials, high power factor and low lattice thermal conductivity are desired properties. Therefore, the high lattice thermal conductivity of two-dimensional materials limits their usage in thermoelectric applications. We employ first-principles calculations along with semiclassical Boltzmann transport theory for the electron and phonon dynamics to investigate the thermoelectric properties of nonmetal-shrouded monolayer Ag2S. We show that the simultaneous presence of flat and dispersive bands in the vicinity of the conduction band edge leads to a high power factor, while close proximity of the acoustic and optical bands in the phonon dispersion results in low thermal conductivity. With moderate electron doping, a high in-plane thermoelectric figure of merit is achieved. Our results demonstrate great potential of nonmetal-shrouded monolayer Ag2S in thermoelectric applications.