  A search for J/psi radiative decay to weakly interacting neutral final states
was performed using the CLEO-c detector at CESR. A total of 3.7 x 10^{6} tagged
J/psi events was collected at the psi(2S) resonance and used to study the decay
J/psi -> gamma+X, where X is a narrow state that is invisible to the detector.
No significant signal was observed and upper limits on the branching fraction
were set for masses m_X up to 960 MeV/c^2. The upper limit corresponding to
m_X=0 is 4.3x 10^{-6} at the 90% confidence level.
