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By analyzing (27.12±0.14)×108 ψ(3686) events accumulated with the BESIII detector, the decay ηc(2S)→K+K−η is observed for the first time with a significance of 6.2σ after considering systematic uncertainties. The product of the branching fractions of ψ(3686)→γηc(2S) and ηc(2S)→K+K−η is measured to be B(ψ(3686)→γηc(2S))×B(ηc(2S)→K+K−η)=(2.39±0.32±0.34)×10−6, where the first uncertainty is statistical, and the second one is systematic. The branching fraction of ηc(2S)→K+K−η is determined to be B(ηc(2S)→K+K−η)=(3.42±0.46±0.48±2.44)×10−3, where the third uncertainty is due to the branching fraction of ψ(3686)→γηc(2S). Using a recent BESIII measurement of B(ηc(2S)→K+K−π0), we also determine the ratio between the branching fractions of ηc(2S)→K+K−η and ηc(2S)→K+K−π0 to be 1.49±0.22±0.25, which is consistent with the previous result of BaBar at a comparable precision level.