The structure of LiCuO has been refined from time-of-flight powder neutron diffraction data in order to define accurately the copper-oxygen coordination geometry and lithium-ion positions. The structure consists of slightly distorted, square-planar CuO units sharing opposite edges to form infinite chains running parallel to the b axis. Lithium ions were found to occupy two types of site in the structure: (1) a distorted tetrahedral site found previously, and (2) two disordered sites displaced from a mean octahedral position. The disorder in the lithium ions is similar to that observed in ferroelectric materials such as LiTaO below their Curie temperature. Bond lengths around copper support its non-integral valence, and bond-valence calculations are performed for all cation sites.