Based on $448.1 times 10^6$ $psi(3686)$ events collected with the BESIII detector, the decays $psi(3686)togammachi_{cJ}, chi_{cJ} to gammagamma~(J=0, 1, 2)$ are studied. The decay branching fractions of $chi_{c0,c2} to gammagamma$ are measured to be $mathcal{B}(chi_{c0}togammagamma) = (1.93 pm 0.08 pm 0.05 pm 0.05)times 10^{-4}$ and $mathcal{B}(chi_{c2}togammagamma) = (3.10 pm 0.09 pm 0.07 pm 0.11)times 10^{-4} $, which correspond to two-photon decay widths of $Gamma_{gammagamma}(chi_{c0}) = 2.03 pm 0.08 pm 0.06 pm 0.13 ~rm{keV}$ and $Gamma_{gammagamma}(chi_{c2}) = 0.60 pm 0.02 pm 0.01 pm 0.04 ~rm{keV}$ with a ratio of $mathcal{R}=Gamma_{gammagamma}(chi_{c2})/Gamma_{gammagamma}(chi_{c0})= 0.295 pm 0.014 pm 0.007 pm 0.027$, where the uncertainties are statistical, systematic and associated with the uncertainties of $mathcal{B}(psi(3686)togammachi_{c0,c2})$ and the total widths $Gamma(chi_{c0,c2})$, respectively. For the forbidden decay of $chi_{c1}togammagamma$, no signal is observed, and an upper limit on the two-photon width is obtained to be $Gamma_{gammagamma}(chi_{c1})<5.3 ~rm{eV}$ at the 90% confidence level. The ratio of the two-photon widths between helicity-zero and helicity-two components in the decay $chi_{c2}togammagamma$ is also measured to be $f_{0/2} = Gamma^{lambda=0}_{gammagamma}(chi_{c2})/Gamma^{lambda=2}_{gammagamma}(chi_{c2}) = (0.0 pm 0.6 pm 1.2)times 10^{-2}$, where the uncertainties are statistical and systematic, respectively.
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