  By analyzing $(27.12 \pm 0.14)\times10^{8}$ $\psi(3686)$ events accumulated
with the BESIII detector, the decay $\eta_{c}(2S) \to K^{+} K^{-} \eta$ is
observed for the first time with a significance of $6.2\sigma$ after
considering systematic uncertainties. The product of the branching fractions of
$\psi(3686) \to \gamma\eta_{c}(2S)$ and $\eta_{c}(2S) \to K^{+} K^{-} \eta$ is
measured to be $\mathcal{B}(\psi(3686) \to\gamma\eta_{c}(2S))\times
\mathcal{B}(\eta_{c}(2S)\to K^{+} K^{-}\eta)=(2.39 \pm 0.32 \pm 0.34) \times
10^{-6}$, where the first uncertainty is statistical, and the second one is
systematic. The branching fraction of $\eta_{c}(2S)\to K^{+} K^{-}\eta$ is
determined to be $\mathcal{B}(\eta_{c}(2S)\to K^{+} K^{-}\eta) = (3.42 \pm 0.46
\pm 0.48 \pm 2.44) \times 10^{-3}$, where the third uncertainty is due to the
branching fraction of $\psi(3686) \to \gamma\eta_{c}(2S)$. Using a recent
BESIII measurement of $\mathcal{B} (\eta_{c}(2S) \to K^{+} K^{-}\pi^{0})$, we
also determine the ratio between the branching fractions of $\eta_{c}(2S) \to
K^{+} K^{-}\eta$ and $\eta_{c}(2S) \to K^{+} K^{-}\pi^{0}$ to be $1.49 \pm 0.22
\pm 0.25$, which is consistent with the previous result of BaBar at a
comparable precision level.
