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Based on a sample of 2.7 × 109 Φ(3686) events collected by the BESIII detector operating at the BEP- CII collider, the decay Φ(3686) → γχcJ, χcJ → ηηη′ is analyzed. The decay modes χc1 and χc2 → ηηη′ are observed for the first time, and their corresponding branching fractions are determined to be ℬ(χc1 → ηηη′)= (1.40±0.13(stat.)±0.09(sys.))× 10-4 and ℬ(χc2 → ηηη′) = (4.18 ± 0.84(stat.) ± 0.48(sys.))× 10-5. An upper limit on the branching fraction of χc0 → ηηη′ set as 2.59 × 10-5 at a 90% confidence level (CL). A partial wave analysis (PWA) of the decay χc1 → ηηη′ is performed to search for the 1-+ exotic state 771 (1855). The PWA result indieates that the structure in the ηη′ mass spectrum is attributed to f0(1500), while in the ηη mass spectrum, it is attributed to the 0++ phase space. The upper limit of ℬ(χc1 → η1 (1855)η)·ℬ(η1(1855) ηη′)