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The decays χcJ → γV (V = φ, ρ 0 , ω) are studied with a sample of radiative ψ ′ → γχcJ events in a sample of (1.06 ± 0.04) × 10 8 ψ ′ events collected with the BESIII detector. The branching fractions are determined to be: B(χc1 → γφ) = (25.8±5.2±2.3)×10 −6 , B(χc1 → γρ 0 ) = (228±13±22)×10 −6 , and B(χc1 → γω) = (69.7 ± 7.2 ± 6.6) × 10 −6 . The decay χc1 → γφ is observed for the first time. Upper limits at the 90% confidence level on the branching fractions for χc0 and χc2 decays into these final states are determined. In addition, the fractions of the transverse polarization component of the vector meson in χc1 → γV decays are measured to be 0.29

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