We report on giant thermopower of S=2.5 mV/K in CoSbS single crystals: a material that shows strong high-temperature thermoelectric performance when doped with Ni or Se. Changes of low-temperature thermopower induced by a magnetic field point to the mechanism of electronic diffusion of carriers in the heavy valence band. Intrinsic magnetic susceptibility is consistent with the Kondo-insulatorlike accumulation of electronic states around the gap edges. This suggests that giant thermopower stems from temperature-dependent renormalization of the noninteracting bands and buildup of the electronic correlations on cooling.