New Physics with three-photon events at LEP

The effect of the most general \z3gt vertex in the reaction $e^+e^- \ra 3\gamma$ is studied with a particular attention to LEP searches. We give exact analytical expressions including realistic cuts for the signal and present a detailed analysis based on a Monte Carlo that includes the effect of the irreducible $3\gamma$ QED cross section. As special applications we discuss the effect of heavy scalars, fermions and gauge bosons and comment on the ``monopole" connection.