We report the first observation of the radiative decay of the ϒ(1S) into a charmonium state. The significance of the observed signal of ϒ(1S)→γχ_{c1} is 6.3 standard deviations including systematics. The branching fraction is calculated to be B[ϒ(1S)→γχ_{c1}]=[4.7_{-1.8}^{+2.4}(stat)_{-0.5}^{+0.4}(sys)×10^{-5}]. We also searched for ϒ(1S) radiative decays into χ_{c0,2} and η_{c}(1S,2S), and set upper limits on their branching fractions. These results are obtained from a 24.9 fb^{-1} data sample collected with the Belle detector at the KEKB asymmetric-energy e^{+}e^{-} collider at a center-of-mass energy equal to the ϒ(2S) mass using ϒ(1S) tagging by the ϒ(2S)→ϒ(1S)π^{+}π^{-} transitions.