Hybrid exchange density functional theory is used to study the wide band gap chalcopyrite CuGaSe 2 .The formation energies of the experimentally observed (4×1) and (1×1) atomic scale reconstructions on the CuGaSe 2 (001) surface are calculated for different environmental conditions. The results suggest that a Serich (1×1) reconstruction, and a Cu-poor, Se-rich (4×1) reconstruction, are the only stable surfaces under all the studied environmental conditions. Two complementary mechanisms for the stabilisation of CuGaSe 2 surfaces are proposed, and it is suggested that the presence of Na stabilises the (4×1) reconstructions, making them the stable terminations under Na-rich conditions.