  We report the results of a search for a charmonium-like state produced in the
process gamma gamma --> omega J/psi in the 3.9-4.2 GeV/c^2 mass region. We
observe a significant enhancement, which is well-described by a resonant shape
with mass M = (3915 +/- 3 +/- 2) MeV/c^2 and total width Gamma = (17 +/- 10 +/-
3) MeV. This enhancement may be related to one or more of the three
charmonium-like states so far reported in the 3.90-3.95 GeV/c^2 mass region.
