Based on 448.1 × 10 6     ψ ( 3686 ) events collected with the BESIII detector, the decays ψ ( 3686 ) → γ χ c J , χ c J → γ γ ( J = 0 , 1 , 2 ) are studied. The decay branching fractions of χ c 0 , 2 → γ γ are measured to be B ( χ c 0 → γ γ ) = ( 1.93 ± 0.08 ± 0.05 ± 0.05 ) × 10 − 4 and B ( χ c 2 → γ γ ) = ( 3.10 ± 0.09 ± 0.07 ± 0.11 ) × 10 − 4 , which correspond to two-photon decay widths of Γ γ γ ( χ c 0 ) = 2.03 ± 0.08 ± 0.06 ± 0.13     keV and Γ γ γ ( χ c 2 ) = 0.60 ± 0.02 ± 0.01 ± 0.04     keV with a ratio of R = Γ γ γ ( χ c 2 ) / Γ γ γ ( χ c 0 ) = 0.295 ± 0.014 ± 0.007 ± 0.027 , where the uncertainties are statistical, systematic and associated with the uncertainties of B ( ψ ( 3686 ) → γ χ c 0 , 2 ) and the total widths Γ ( χ c 0 , 2 ) , respectively. For the forbidden decay of χ c 1 → γ γ , no signal is observed, and an upper limit on the two-photon width is obtained to be Γ γ γ ( χ c 1 ) < 5.3     eV at the 90% confidence level. The ratio of the two-photon widths between helicity-zero and helicity-two components in the decay χ c 2 → γ γ is also measured to be f 0 / 2 = Γ λ = 0 γ γ ( χ c 2 ) / Γ λ = 2 γ γ ( χ c 2 ) = ( 0.0 ± 0.6 ± 1.2 ) × 10 − 2 , where the uncertainties are statistical and systematic, respectively.