  We report the first observation of the doubly Cabibbo-suppressed decay
$D^+_s\to K^+K^+\pi^-$ using 605 fb$^{-1}$ of data collected with the Belle
detector at the KEKB asymmetric-energy $e^+e^-$ collider. The branching ratio
with respect to its Cabibbo-favored counterpart $\mathcal{B}(D^+_s\to
K^+K^+\pi^-)$ / $\mathcal{B}(D^+_s\to K^+K^-\pi^+)$ is
(0.229$\pm0.028\pm$0.012)%, where the first uncertainty is statistical and the
second is systematic. We also report a significantly improved measurement of
the doubly Cabibbo-suppressed decay $D^+\to K^+\pi^+\pi^-$, with a branching
ratio $\mathcal{B}(D^+\to K^+\pi^+\pi^-)$ / $\mathcal{B}(D^+\to
K^-\pi^+\pi^+)$=(0.569$\pm0.018\pm$0.014)%.
