A quaternary compound, Na15Cu3Ga6S18, the first member in the A-Cu-Ga-S (A = alkali metal) series, has been synthesized from a solid-state metathesis reaction between Na6Ga2S6 and CuCl as well as from a combination of Na2S, Ga, Cu, and S. The compound crystallizes in a monoclinic crystal system, space group C2/c, and represents a unique open-framework structure with channels filled with eight crystallographically distinct Na ions. The anionic framework is built up of infinite chains of corner-shared GaS4 tetrahedra fused together by an edge-shared dimer of CuS4 tetrahedra forming one-dimensional ribbons of (Cu2Ga6S18)16-, which are cross-linked by linearly coordinated S-Cu-S linkages resulting in a three-dimensional network with tunnels filled with Na atoms. Optical band gap measurements show that the compound has a direct band gap of 3.00 eV that is in good agreement with the theoretical band gap derived from density functional theory calculations. Band structure calculations further indicate that the states near the Fermi level are dominated by tetrahedral Cu+(d) and S(p) states resulting from the antibonding interactions, while s-d hybridization is prevalent in linear Cu+ coordination. Ionic conductivity measurements show that the compound has a room-temperature Na ion conductivity of 2.72 x 10-5 mS/cm with an activation energy of 0.68 eV, which corroborates well the nudged elastic band calculations.