In a study of B+-> J/psi gamma K+ decays, we find evidence for the radiative decay X(3872)-> J/psi gamma with a statistical significance of 3.4 sigma. We measure the product of branching fractions B(B+-> X(3872)K+)center dot B(X(3872)-> J/psi gamma)=(3.3 +/- 1.0 +/- 0.3)x10(-6), where the uncertainties are statistical and systematic, respectively. We also measure the branching fraction B(B+->chi K-c1(+))=(4.9 +/- 0.2 +/- 0.4)x10(-4). These results are obtained from (287 +/- 3) million B (B) over bar decays collected at the Upsilon(4S) resonance with the BABAR detector at the PEP-II B Factory at SLAC
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