An X-ray single-crystal determination of the CuO structure has been made at 196 K, i.e. below the Neel temperature 230 K, and, as a check, the crystal structure at room temperature was also determined. The correct space group for the structure at both temperature was found to be Cc. Earlier results of magnetic and neutron diffraction measurements can be explained as antiferromagnetic coupling between copper atoms via oxygen (superexchange) in chains running in the (1 0-1) direction. The structural results show changes with temperature in Cu-O distance in these chains: in each -Cu-O-Cu-group the longer is increased and the shorter decreased when passing from 196 K to room temperature. This implies a weaker antiferromagnetic coupling at room temperature. The refinement of CuO-structure at room temperature reported earlier by Asbrink and Norrby (1970) showed the symmetry to be C2/c. An attempt to refine CuO in the space group Cc with the old data was not successful. The different results obtained with different crystals are tentatively explained from published observations regarding valence fluctuations in CuO and non-stoichiometry caused by cation vacancies.