We report the discovery of the first known probable case of a physical triple quasar (not a gravitational lens). A previously known double system, QQ 1429-008 at z = 2.076, is shown to contain a third, fainter QSO component at the same redshift within the measurement errors. Deep optical and IR imaging at the Keck and VLT telescopes has failed to reveal a plausible lensing galaxy group or a cluster, and moreover, we are unable to construct any viable lensing model which could lead to the observed distribution of source positions and relative intensities of the three QSO image components. Furthermore, there are hints of differences in broad-band spectral energy distributions of different components, which are more naturally understood if they are physically distinct AGN. Therefore, we conclude that this system is most likely a physical triple quasar, the first such close QSO grouping known at any redshift. The projected component separations in the restframe are ~ 30 - 50 kpc for the standard concordance cosmology, typical of interacting galaxy systems. The existence of this highly unusual system supports the standard picture in which galaxy interactions lead to the onset of QSO activity.