Low-temperature specific heat measurements and dielectric spectroscopy have been performed on polycrystalline and single-crystalline FeCr2S4, the single crystals showing a transition into a low-temperature orbital glass phase. The freezing of the orbital moments is revealed by a glasslike specific heat anomaly and by a clear relaxational behavior of the dielectric permittivity, exhibiting several hallmark features of glassy dynamics. The orbital relaxation dynamics continuously slows down over six decades in time, before at the lowest temperatures the glass transition becomes suppressed by quantum tunneling.