Using a sample of e⁺e⁻ annihilation events collected with the L3 detector at the Z resonance corresponding to an integrated luminosity of 137 pb⁻¹, we have searched for anomalous production of γX final states where X represents stable, weakly interacting particles and the photon energy is greater than 15 GeV. The sample of events found is consistent with Standard Model expectations. Upper limits are set on Zγ couplings, the τ neutrino magnetic moment, and the branching ratio for Z → γX.