By analyzing (27.12±0.14)×108 ψ(3686) events collected with the BESIII detector operating at the BEPCII collider, the decay processes χcJ→3(K+K-) (J=0, 1, 2) are observed for the first time with statistical significances of 8.2σ, 8.1σ, and 12.4σ, respectively. The product branching fractions of ψ(3686)→γχcJ, χcJ→3(K+K-) are presented and the branching fractions of χcJ→3(K+K-) decays are determined to be Bχc0→3(K+K-)=(10.7±1.8±1.1)×10-6, Bχc1→3(K+K-)=(4.2±0.9±0.5)×10-6, and Bχc2→3(K+K-)=(7.2±1.1±0.8)×10-6, where the first uncertainties are statistical and the second are systematic.