We report the synthesis of single crystals of the quaternary sulfide, BaCeCuS₃, for the first time by heating a polycrystalline sample of BaCeCuS₃ with an excess of KCl flux inside a vacuum-sealed fused silica tube. The crystal structure of the compound is determined by a single-crystal X-ray diffraction study which shows that it crystallizes in the primitive orthorhombic crystal system (space group: Pnma) with cell constants of a = 10.6740(13) Å, b = 4.1200(6) Å, and c = 13.409(2) Å. The structure is best described as a pseudo-two-dimensional structure where tetrahedral CuS₄ and octahedral CeS₆ units serve as the main building blocks. The polyanionic layers in the structure are separated by the presence of electropositive Ba²⁺ cations. The optical absorption study on the polycrystalline sample of BaCeCuS₃ shows a semiconducting nature with a direct bandgap of 1.8(2) eV consistent with the green color of the sample. The temperature-dependent thermal conductivity (k_tot) measurements on the polycrystalline BaCeCuS₃ sample reveal an extremely low value of k_tot (0.32 W m⁻¹ K⁻¹) at 773 K. DFT calculations were carried out to obtain the electronic structure of the title compound. Our theoretical studies predict a high value of the thermoelectric figure of merit (>1) for BaCeCuS₃ by optimization of the charge carriers. To also explore a practical application of BaCeCuS₃, a liquid junction solar cell was fabricated: TiO₂/CdS/BaCeCuS₃/S_n²⁻/S²⁻/MWCNTs@Ni, and the cell delivered an efficiency enhanced by ∼45% compared to the one without the sulfide. The performance improvement is affected by the hole conducting properties of BaCeCuS₃, which allows facile hole transfer from CdS to the polysulfide, increases the charge separation, and hence increases the efficiency.