Discovering new candidate p-type transparent conducting oxides has become a major goal for material scientists. Recently delafossite CuBO2 has been proposed as a promising candidate, showing good room temperature electrical conductivity and excellent transparency [Appl. Phys. Lett. 2007, 91, 092123]. In this article we report a density functional theory investigation of CuBO2, examining the geometry and electronic structure using GGA corrected for on-site Coulomb interactions (GGA U) and a hybrid density functional (HSE06). From analysis of the calculated band structure, density of states, and optical absorption, we predict an indirect fundamental band gap of 3.1 eV and a direct optical band gap of 3.6 eV. The hole effective mass at the valence band maximum indicates the potential for good p-type conductivity, consistent with the reported experimental results. These results are discussed in relation to other delafossite oxides.