By analyzing (2.712±0.014)×10⁹ $ψ(3686)$ events collected by the BESIII detector, we report the first experimental study of the decays χcJ→ p K⁻ K⁻ Ξ⁺+c.c.~(J=0,1,2). The decays χc1→ p K⁻ K⁻ Ξ⁺+c.c. and χc2→ p K⁻ K⁻ Ξ⁺+c.c. are observed for the first time with significances of $9.0σ$ each, and their branching fractions are determined to be B_χc1→ p K⁻ K⁻ Ξ⁺+c.c. =(9.6+2.2-2.0±0.8)×10⁻⁶, and B_χc2→ p K⁻ K⁻ Ξ⁺+c.c. =(7.5+1.8-1.5±0.5)×10⁻⁶, where the first and second uncertainties are statistical and systematic, respectively. No significant signal is observed for χc0→ p K⁻ K⁻ Ξ⁺+c.c., and an upper limit on its branching fraction of 12.7×10⁻⁶ is established at the 90% confidence level.
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