  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.
