  We report a giant thermoelectric figure of merit $ZT$ (up to 6 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 Gr\"uneisen-parameter spectrum. The main source of the large $ZT$ 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.
