Two-dimensional (2D) materials with lower lattice thermal conductivities and high figures of merit are useful for applications in thermoelectric (TE) devices. In this work, the thermoelectric properties of monolayer Cu₂S and Cu₂Se are systematically studied through first-principles and Boltzmann transport theory. The dynamic stability of monolayer Cu₂S and Cu₂Se through elastic constants and phonon dispersions are verified. The results show that monolayer Cu₂S and Cu₂Se have small lattice constants, resulting in lower phonon vibration modes. Phonon transport calculations confirm that monolayer Cu₂Se has lower lattice thermal conductivity (1.93 W/(m·K)) than Cu₂S (3.25 W/(m·K)) at room temperature, which is due to its small Debye temperature and stronger anharmonicity. Moreover, the heavier atomic mass of Se atom effectively reduces the phonon frequency, resulting in an ultra narrow phonon band gap (0.08 THz) and a lower lattice thermal conductivity for monolayer Cu₂Se. The band degeneracy effect at the valence band maximum (VBM) of monolayer Cu₂S and Cu₂Se significantly increase their carrier effective mass, resulting in higher Seebeck coefficients and lower conductivities under p-type doping. The electric transport calculation at room temperature shows that the conductivity of monolayer Cu₂S (Cu₂Se) under n-type doping about 10¹¹ cm^–2 is 2.8×10⁴ S/m (4.5×10⁴ S/m), obviously superior to its conductivity about 2.6×10² S/m (1.6×10³ S/m) under p-type doping. At the optimum doping concentration for monolayer Cu₂S (Cu₂Se), the n-type power factor is 16.5 mW/(m·K²) (25.9 mW/(m·K²)), which is far higher than p-type doping 1.1 mW/m·K² (6.6 mW/(m·K²)). Through the above results, the excellent figure of merit of monolayer Cu₂S (Cu₂Se) under optimal n-type doping at 700 K can approach to 1.85 (2.82), which is higher than 0.38 (1.7) under optimal p-type doping. The excellent thermoelectric properties of monolayer Cu₂S (Cu₂Se) are comparable to those of many promising thermoelectric materials reported recently. Especially, the figure of merit of monolayer Cu₂Se is larger than that of the well-known high-efficient thermoelectric monolayer SnSe (2.32). Therefore, monolayer Cu₂S and Cu₂Se are potential thermoelectric materials with excellent performances and good application prospects. These results provide the theoretical basis for the follow-up experiments to explore the practical applications of 2D thermoelectric semiconductor materials and provide an in-depth insight into the effect of phonon thermal transport on improvement of TE transport properties.