As the demand for photovoltaics rapidly increases, there is a pressing need for the identification of new visible light absorbing materials for thin-film solar cells that offer similar performance to the current technologies based on CdTe and Cu(In,Ga)Se(2). Metal sulphides are the ideal candidate materials, but their band gaps are usually too large to absorb significant fractions of visible light. However, by combining Cu(+) (low binding energy d(10) band) and Sb(3+)/Bi(3+) (low binding energy s(2) band), the ternary sulphides CuSbS(2) and CuBiS(2) are formed, which have been gathering recent interest for solar cell applications. Using a hybrid density functional theory approach, we calculate the structural and electronic properties of these two materials. Our results highlight the stereochemical activity of the Sb and Bi lone pair electrons, and predict that the formation of hole carriers will occur in the Cu d(10) band and hence will involve oxidation of Cu(I).