The possible existence of group 6 TM3 compounds with T = Cr, Mo, W and M = Ga, In is investigated with the aid of density functional theory calculations. Their most probable crystal structure is expected to be of the FeGa3 type tetragonal space group P42/mnm. All compounds are computed to be semiconductors with a band gap ranging from 0.08 to 0.43 eV, at the modified Becke-Johnson level of theory. The thermoelectric properties are analyzed via calculations based on Boltzmann transport equation under a constant relaxation time approximation. Promising power factors are computed for both n- and p-type WGa3 because of a band degeneracy around the Fermi level similar to that of heavily doped PbTe and SnTe materials. If the optimal chemical potential can be reached, a thermoelectric figure of merit up to 0.6 at 800 K for both n- and p-type may be expected for WGa3.