The crystal structure of a ternary sulfide with the approximate composition LiCuS, which is a promising candidate for environment-friendly battery and solar cell materials is reported. The crystal structure was solved by a combination of neutron and X-ray powder diffraction data and 7 Li solid-state NMR analysis. A yellow powder, Li1.1Cu0.9S, was obtained by the reaction of CuS with a slight excess of Li metal. The compound crystallizes in the Na3AgO2 structure type in the space group Ibam. An idealized crystal structure of Li1.1Cu0.9S can be derived from the cubic Li2S structure by moving a part of the Li along the c axis so that these Li atoms become linearly coordinated by S. All the metal sites are occupied by randomly mixed Li and Cu atoms; however, there is a strong preference for linear coordination by Cu. The density functional theory calculations show that Li1.1Cu0.9S is a direct band-gap semiconductor with an energy gap of 1.95 eV in agreement with experimental data.