Using a total of 2.74×107 decays of the ψ(2S) collected with the CLEO-c detector, we present a study of χcJ→γV, where V=ρ0, ω, □. The transitions χc1→γρ0 and χc1→γω are observed with B(χc1→γρ0)=(2. 43±0.19±0.22)×10-4 and B(χc1→γω)=(8. 3±1.5±1.2)×10-5. In the χc1→γρ0 transition, the final state meson is dominantly longitudinally polarized. Upper limits on the branching fractions of other χcJ states to light vector mesons are presented.