The structure of a non-stoichiometric copper compound Cu1.8S (digenite) has been studied by X-ray diffraction. Although digenite has a cubic anti-fluorite structure, satellite reflections were seen along the (111)c axis. Single-crystal X-ray diffraction data, including first- and second-order satellites, were collected using a four-circle diffractometer. A rhombohedral twinning model was used to determine the modulation densities of the copper ions. The final R-factor is about 10% including the main and satellite reflections. The present analysis shows that the crystal is composed of domain-like structures: in each domain, the dimensions of the regular lattice, formed from copper ions, are slightly larger than those of the basic sulphur lattice. The origin of this domain-like structure, based on the Frenkel-Kontorova model, is attributed to the non-stoichiometry and apparently smaller cation-anion interaction.