Abstract: Doped Cr2O3 has been shown to be a p-type transparent conducting oxide (TCO). Its conductivity, however, is low. As for most p-type TCOs, the main problem is the high effective hole mass due to flat valence bands. We use first-principles methods to investigate whether one can increase the valence band dispersion (i.e. reduce the hole mass) by anion alloying with sulfur, while keeping the band gap large enough for transparency. The alloying concentrations considered are given by Cr(4)SxO(6-x), with x = 1-5. To be able to describe the electronic properties of these materials accurately, we first study Cr2O3, examining critically the accuracy of different density functionals and methods, including PBE, PBE+U, HSE06, as well as perturbative approaches within the GW approximation. Our results demonstrate that Cr4S2O4 has an optical band gap of 3.08 eV and an effective hole mass of 1.8 m(e). This suggests Cr4S2O4 as a new p-type TCO host candidate.