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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.