We report the first observation of the decay J/psi --> 3 gamma. The signal has a statistical significance of 6 sigma and corresponds to a branching fraction of B(J/psi --> 3 gamma) = (1.2 +- 0.3 +- 0.2) x 10^-5, in which the errors are statistical and systematic, respectively. The measurement uses psi(2S) --> pi+ pi- J/psi events acquired with the CLEO-c detector operating at the CESR e+e- collider.
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