The thermoelectric transport properties of two-dimensional (2D) layered NaCuX (X = S, Se) are investigated by employing first-principles based Boltzmann transport theory. Single quintuple NaCuX layers have a relatively large Seebeck coefficient (S), electrical conductivity (σ) and hence power factor (PF = S2σ) for a p-type heavy doped region due to the valence band degeneracy. The largely reduced σ by dominant polar scattering leads to a PF up to 0.27 and 0.84 mW m-1 K-2 at 1200 K for p-type NaCuS and NaCuSe monolayers, respectively. The high polarizability of the Cu-X bonds in the CuX4 tetrahedra leads to anharmonic phonon behavior which produces an intrinsic lattice thermal conductivity (κl) as low as 1.03 and 0.75 W m-1 K-1 at 300 K for NaCuS and NaCuSe, respectively. The predicted figure of merit (zT) increases monotonically from around 0.25 at 300 K to 2.01 at 1200 K at an optimal carrier density of around 1 × 1013 cm-2 for p-type NaCuSe and from around 0.09 at 300 K to 1.15 at 1200 K at an optimal carrier density of around 1 × 1014 cm-2 for p-type NaCuS. These findings indicate that the NaCuS, especially NaCuSe, monolayers are promising 2D thermoelectric materials persisting at high temperature.