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.
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