The possibility of stably anchoring dye molecules on the exposed surface of a p-type semiconductor is crucial to have efficient dye-sensitized photoelectrodes. Here, we theoretically characterize the adsorption mechanism of carboxylic and phosphonic anchoring groups onto the (012) surface of stoichiometric and reduced CuCrO 2 delafossite. Density Functional Theory is employed to accurately predict the preferred adsorption modes and their energies, both in gas phase and solution (water and acetonitrile). On the stoichiometric (012) surface, we found a strong selectivity toward the molecular monodentate binding modes at the highly active Cr-sites, stabilized by strong Hydrogen-bonds with the surface oxygens, for both anchoring groups; deprotonated bidentate bridging anchoring is only identified when the proton transferred to the surface is kept far away from the molecule during the structural relaxation process. On the other hand, the bidentate anchoring becomes the preferred adsorption mode when Cu + vacancies are considered at the topmost layer of the surface slab. The identification of stable bidentate bridging anchoring modes on the CuCrO 2 surface might have important implications for the device stability, as well as for the efficiency of the interfacial hole injection and suggest it as an alternative material to NiO for p-type DSSCs.