We report the branching ratios of the χc2(13P2) and χc0(13P0) charmonium resonances to two photons using event samples collected by Fermilab experiment E835 in the reactions p¯p→χc2(13P2)[χc0(13P0)]. Our result for the χc2 is B(χc2→γγ)=(1.35±0.25±0.12)×10−4. We set a 95% upper limit for the χc0 branching ratio B(χc0→γγ) at 2.09×10−4.