Based on (2712.4 ± 14.3) x 10⁶ e⁺e^- → ψ(3686) events collected with the BESIII detector operating at the BEPCII Collider, we report the first evidence of χ_c0 → ΛΛ<over bar>Φ decays and the first observation of χ_c1,2 → ΛΛ<over bar>Φ decays, with significances of 4.1σ, 11.3σ and 13.0σ, respectively. The decay branching fractions of χ_c0,1,2 → ΛΛ<over bar>Φ are measured to be (2.99 ± 1.24 ± 0.19) x 10^-5, (6.01 ± 0.90 ± 0.40) x 10^-5, and (7.13 ± 0.81 ± 0.36) x 10^-5, where the first uncertainties are statistical and the second systematic. No obvious enhancement near the ΛΛ<over bar> production threshold or excited Λ state is found in the ΛΦ (or Λ<over bar>Φ) system.