We report a giant thermoelectric figure of merit Z T (up to six at 1100 K) in n-doped lanthanum oxysulphate LaSO. Thermoelectric coefficients are computed from ab initio bands within Bloch-Boltzmann theory in an energy-, chemical potential-, and temperature-dependent relaxation time approximation. The lattice thermal conductivity is estimated from a model employing the ab initio phonon and Grüneisen-parameter spectrum. The main source of the large Z T is the significant power factor which correlates with a large band complexity factor. We also suggest a possible n-type dopant for the material based on ab initio calculations.