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The transitions chi_c1 -> gamma rho^0 and chi_c1 -> gamma omega are observed with B(chi_c1 -> gamma rho^0) = (2.43 +- 0.19 +- 0.22) x 10^-4 and B(chi_c1 -> gamma omega) = (8.3 +- 1.5 +- 1.2) x 10^-5. In the chi_c1 -> gamma rho^0 transition, the final state meson is dominantly longitudinally polarized. 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