The crystal structure of superconducting (37.5 K) La2CuO4.032 has been refined from single-crystal neutron-diffraction data at room temperature and 15 K. At both temperatures it exhibits the orthorhombic symmetry Cmca. The extra oxygen O4 atoms occupy the special positions ( 1 4y 1 4 with y=0.243 at 15 K). They are located between two successive LaO layers and are surrounded by distorted cubes built up of two interpenetrated tetrahedra, one comprising four La atoms and the other four O1 atoms (the apical oxygen atoms of the CuO6octahedra). The O4 insertion causes a 0.75 Å displacement of 4.8% of the O1 atoms towards new O3 positions (x=0.030(5), y=0.182(2), z=0.100(5)). From the refined values of the occupancy factors at 15 K, it is deduced that for each extra O4 three O1 are displaced to O3 with one short O3-O4 distance of 1.64(3) Å. This value indicates the formation of a strong O-O covalent bond of peroxide type with a formal 2-valence. Since the La and Cu sublattices have been found to be fully occupied and the doping does not change the oxygen charge, the La, Cu and O sublattices have the formal valences 6+, 2+, and 8-, respectively. However, the increase in La coordination and the consequent La-O distance readjustment indicate, when compared to the undoped compound structure, that a charge transfer occurs in La2CuO4.032, with the excess positive charge going either to the La or to the O sublattice. In the latter case it would correspond to the formation of holes in the O 2p band. © 1989.