  The singly Cabibbo-suppressed decay $\Lambda_{c}^{+}\to
\Sigma^{-}K^{+}\pi^{+}$ is observed for the first time with a statistical
significance of $6.4\sigma$ by using 4.5 fb$^{-1}$ of $e^+e^-$ collision data
collected at center-of-mass energies between 4.600 and 4.699 GeV with the
BESIII detector at BEPCII. The absolute branching fraction of
$\Lambda_{c}^{+}\to \Sigma^{-}K^{+}\pi^{+}$ is measured to be $(3.8\pm1.3_{\rm
stat}\pm0.2_{\rm syst})\times 10^{-4}$ in a model-independent approach. This is
the first observation of a Cabibbo-suppressed $\Lambda_{c}^{+}$ decay involving
$\Sigma^-$ in the final state. The ratio of branching fractions between
$\Lambda_{c}^{+}\to \Sigma^{-}K^{+}\pi^{+}$ and the Cabibbo-favored decay
$\Lambda_{c}^{+}\to \Sigma^- \pi^+\pi^+$ is calculated to be $(0.4 \pm
0.1)s_{c}^{2}$, where $s_{c} \equiv \sin\theta_c = 0.2248$ with $\theta_c$ the
Cabibbo mixing angle. This ratio significantly deviates from $1.0s_{c}^{2}$ and
provides important information for the understanding of nonfactorization
contributions in $\Lambda_{c}^{+}$ decays.
