Of the simple diatomic molecules, oxygen is the only one to carry a magnetic moment. This makes solid oxygen particularly interesting: it is considered a 'spin-controlled' crystal1 that displays unusual magnetic order2. At very high pressures, solid oxygen changes from an insulating to a metallic state3; at very low temperatures, it even transforms to a superconducting state4. Structural investigations of solid oxygen began in the 1920s and at present, six distinct crystallographic phases are established unambiguously1. Of these, the phase of solid oxygen is particularly intriguing: it exhibits a dark-red colour, very strong infrared absorption, and a magnetic collapse1. It is also stable over a very large pressure domain and has been the subject of numerous X-ray diffraction5,6,7, spectroscopic8,9,10,11 and theoretical studies12,13,14. But although -oxygen has been shown to have a monoclinic C2/m symmetry5,6,7,15 and its infrared absorption behaviour attributed to the association of oxygen molecules into larger units9,14, its exact structure remains unknown. Here we use single-crystal X-ray diffraction data collected between 13 and 18 GPa to determine the structure of -oxygen. We find that -oxygen is characterized by the association of four O2 molecules into a rhombohedral molecular unit, held together by what are probably weak chemical bonds. This structure is consistent with existing spectroscopic data, and further validated by the observation of a newly predicted Raman stretching mode.