Using an e+e- collision data sample of (27.08±0.14)×108 ψ(3686) events collected by the BESIII detector, we report the first observation of χcJ→ω-ω¯+ (J=0, 1, 2) decays with significances of 5.6σ, 6.4σ, and 18σ, respectively, where the χcJ mesons are produced in the radiative ψ(3686) decays. The branching fractions are determined to be B(χc0→ω-ω¯+)=(3.51±0.54±0.29)×10-5, B(χc1→ω-ω¯+)=(1.49±0.23±0.10)×10-5, and B(χc2→ω-ω¯+)=(4.52±0.24±0.18)×10-5, where the first and second uncertainties are statistical and systematic, respectively.