In a study of B + → J / ψ γ K + decays, we find evidence for the radiative decay X ( 3872 ) → J / ψ γ with a statistical significance of 3.4 σ . We measure the product of branching fractions B ( B + → X ( 3872 ) K + ) ⋅ B ( X ( 3872 ) → J / ψ γ ) = ( 3.3 ± 1.0 ± 0.3 ) × 10 − 6 , where the uncertainties are statistical and systematic, respectively. We also measure the branching fraction B ( B + → χ c 1 K + ) = ( 4.9 ± 0.2 ± 0.4 ) × 10 − 4 . These results are obtained from ( 287 ± 3 ) million B ¯¯¯ B decays collected at the Υ ( 4 S ) resonance with the BABAR detector at the PEP-II B Factory at SLAC.