Jupiter has a giant magnetosphere that is coupled to the planet's upper atmosphere; as the planet rotates, its magnetic field drags a dense ionized equatorial sheet of plasma, which must interact with the upper atmosphere. Jupiter's aurorae are much more powerful than the Earth's, and cause significant local heating of the upper atmosphere. Auroral electrojets - ion winds that race around Jupiter's auroral ovals - play a key role in theoretical models of how Jupiter's rotational energy is transferred to the plasma sheet and how winds may transport energy from auroral heating to lower latitudes. But there has hitherto been no direct observational evidence for the existence of such electrojets. Here we report observations of electrojets that have winds approaching or in excess of the local speed of sound. The energy produced by these electrojets could heat the whole upper atmosphere, if the auroral regions couple efficiently with the rest of the planet.