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Using 448.1 × 106 ψ(3686) decays collected with the BESIII detector at the BEPCII e+e− storage rings, the branching fractions and angular distributions of the decays χcJ → Ξ−Ξ¯¯¯¯+ and Ξ0Ξ¯¯¯¯0 (J = 0, 1, 2) are measured based on a partial-reconstruction technique. The decays χc1 → Ξ0Ξ¯¯¯¯0 and χc2 → Ξ0Ξ¯¯¯¯0 are observed for the first time with statistical significances of 7σ and 15σ, respectively. The results of this analysis are in good agreement with previous measurements and have significantly improved precision.