A search for radiative decays of the P-wave spin singlet charmonium resonance hc is performed based on 4.48×108 ψ′ events collected with the BESIII detector operating at the BEPCII storage ring. Events of the reaction channels hc→γη′ and γη are observed with a statistical significance of 8.4σ and 4.0σ, respectively, for the first time. The branching fractions of hc→γη′ and hc→γη are measured to be B(hc→γη′)=(1.52±0.27±0.29)×10−3 and B(hc→γη)=(4.7±1.5±1.4)×10−4, respectively, where the first errors are statistical and the second are systematic uncertainties.