We report here on the discovery of supersonic Evershed downflows in the penumbra of a sunspot. These flows are shown to occur along spatially unresolved, very cold magnetic flux tubes whose downflowing footpoints are found from the middle penumbra outward. Evershed flows along magnetic field lines returning to the solar surface were discovered by Westendorp Plaza and coworkers, but only in the outer parts of the penumbra and beyond its visible boundary; on the other hand, no supersonic flows of any type have ever been reported in the photosphere of sunspots, except for the very different case of the delta spot analyzed by Martínez Pillet and coworkers. We present unequivocal evidence of such supersonic motions, already predicted theoretically by the siphon-flow model, from the interpretation of infrared spectropolarimetric observations of a sunspot with unprecedented spatial resolution.