The temperature-dependence of the band gap of the proposed photovoltaic absorber copper antimony sulphide (CuSbS2) has been studied by Fourier-transform infrared spectroscopy. The direct gap rises from 1.608 to 1.694 eV between 300 and 4.2 K. Below 200 K an exciton-like feature develops above the absorption edge at 1.82 eV. First-principles calculations evaluate band structure, band symmetries, and dipole selection rules, suggesting distinctly enhanced absorption for certain excitonic optical transitions. Striking consistency is seen between predicted dielectric and absorption spectra and those determined by ellipsometry, which reveal rapidly strengthening absorption passing 105 cm−1 at 2.2 eV. These results suggest beneficial photovoltaic performance due to strong optical absorption arising from unusually strong electron–hole interactions in polycrystalline CuSbS2 material.