In this work, we studied the effect of the triethanolamine (TEA) concentration on the physicochemical properties of copper sulfide (CuS) thin films deposited by the ammonia-free chemical bath deposition method (CBD). CuS thin films were characterized in an as-deposited state and annealing at 70 °C/6 h. Raman spectroscopy evidenced the S–S stretching mode associated with the hexagonal structure (covellite) of CuS. The microstructural analysis showed that the TEA concentration and the thermal treatment strongly influence the surface morphology. The surface roughness varied from 6.4 to 14.0 nm. The band gap ( E g ), thickness ( d ), and optical constants ( n and k ) were estimated by simulating the transmission ( T ) and reflection ( R ) spectra. Notably, the thermally treated CuS thin films are thinner when the TEA concentration increases due to the densification phenomenon. The chemical states of elements and the S/Cu ratio on the surface of the CuS films were assessed by X-ray photoelectron spectroscopy (XPS). The electrical properties of the CuS thin films as a function of TEA concentration and thermal treatment were characterized using the Hall effect. These results show the importance of the complexing agent (TEA) and low-temperature thermal treatment on the physicochemical properties of CuS thin films.