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' crystal that displays unusual magnetic order. At very high pressures, solid oxygen changes from an insulating to a metallic state; at very low temperatures, it even transforms to a superconducting state. Structural investigations of solid oxygen began in the 1920s and at present, six distinct crystallographic phases are established unambiguously. Of these, the ∊ phase of solid oxygen is particularly intriguing: it exhibits a dark-red colour, very strong infrared absorption, and a magnetic collapse. It is also stable over a very large pressure domain and has been the subject of numerous X-ray diffraction, spectroscopic and theoretical studies. But although ∊-oxygen has been shown to have a monoclinic C2/m symmetry and its infrared absorption behaviour attributed to the association of oxygen molecules into larger units, its exact structure remains unknown. Here we use single-crystal X-ray diffraction data collected between 13 and 18GPa 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.