Ternary chalcostibite (CuSbS2) is a non-toxic and earth-abundant thin-film solar cell material with an optimal band gap, high optical absorption coefficient, and p-type electrical conductivity. Large-grained CuSbS2 thin films are crystallized by sulfurizing thermally evaporated Cu/Sb/Cu precursor stacks at 450 °C for a short duration of 1–10 min. The precursor stacks sulfurized at 450 °C for 1 min resulted in the formation of a Cu-deficient (to a small extent) and Sb-rich large-grained thin-films of CuSbS2 without any secondary phases. Increasing the sulfurization duration from 5 min to 10 min resulted in the formation of near-stoichiometric CuSbS2 films with columnar growth and more uniformly sized grains. The direct band gap of the films is found to be 1.42 eV. The electrical resistivity decreases from 28.6 to 16.7 Ω cm upon increasing the sulfurization duration from 1 to 10 min, respectively, and the hole mobility is in the range of 0.44–0.56 cm2 V−1 s−1. The solar cells fabricated using the CuSbS2 films sulfurized for a duration of 5 min exhibited a maximum power conversion efficiency of 2.5% with an open-circuit voltage of 568.7 mV and a short-circuit current density of 13.8 mA/cm2. This study provides a pathway for the development of high-efficiency CuSbS2 solar cells.