Total neutron diffraction studies show that the layered lithium molybdate, (LiMoO2)-O-III, contains zigzag molybdenum chains within the MoO2 layers. The short distances along the zigzag, d(Mo-Mo) = 2.618 Angstrom, are indicative of strong metal-metal bonds. The structure adopted is in agreement with theoretical predictions for a d(3) metal system and differs from that previously published. The average structure is best described in the space group C2/m, with a = 10.543(6) Angstrom, b = 2.8626(5) Angstrom, c = 10.899(6) Angstrom, and beta = 153.29(1)degrees. The utility of determining radial correlation functions from diffraction data as a check on the final structure obtained from Bragg scattering studies of polycrystalline materials is demonstrated.