We have observed single-nucleus quantum beats in the incoherent scattering of synchrotron radiation by the 14.4 keV transition of ⁵⁷Fe. The 20 ns beat period characteristic of the nuclear excited-state splitting was clearly seen when enriched metallic samples were excited at the nuclear resonance energy or far from the resonance energy (i.e. accompanied by phonon excitation). The phase of the beat pattern is seen to change with the scattering angle in a manner consistent with the angular-momentum change of the (M1) transition.