  We present the first measurement of the branching fraction of the singly
Cabibbo-suppressed (SCS) decay $\Lambda_c^+ \to p \eta'$ with $\eta' \to
\eta\pi^+\pi^-$, using a data sample corresponding to an integrated luminosity
of 981 $\rm fb^{-1}$, collected by the Belle detector at the KEKB
$e^{+}$$e^{-}$ asymmetric-energy collider. A significant $\Lambda_c^+$ signal
is observed for the first time with a signal significance of 5.4$\sigma$. The
relative branching fraction with respect to the normalization mode $\Lambda_c^+
\to pK^-\pi^+$ is measured to be
  \begin{equation*}
  \frac{{\cal B}(\Lambda_c^+ \to p \eta')}{{\cal B}(\Lambda_c^+ \to p
K^-\pi^+)} = (7.54 \pm 1.32 \pm 0.75) \times 10^{-3},
  \end{equation*}
  where the uncertainties are statistical and systematic, respectively. Using
the world-average value of ${\cal B}(\Lambda_c^+ \to p K^-\pi^+) =
(6.28\pm0.32)\times10^{-2}$, we obtain
  \begin{equation*}
  {\cal B}(\Lambda_c^+ \to p \eta') = (4.73 \pm 0.82 \pm 0.47 \pm 0.24)\times
10^{-4},
  \end{equation*}
  where the uncertainties are statistical, systematic, and from ${\cal
B}(\Lambda_c^+ \to pK^-\pi^+)$, respectively.
