  The decay $\Lambda_b^0 \to \Lambda_c^+ p \overline{p} \pi^-$ is observed
using $pp$ collision data collected with the LHCb detector at centre-of-mass
energies of $\sqrt{s}=$ 7 and 8 TeV, corresponding to an integrated luminosity
of 3 $fb^{-1}$. The ratio of branching fractions between $\Lambda_b^0 \to
\Lambda_c^+ p \overline{p} \pi^-$ and $\Lambda_b^0 \to \Lambda_c^+ \pi^-$
decays is measured to be \begin{equation*}
  \frac{\mathcal{B}(\Lambda_b^0 \to \Lambda_c^+ p
\overline{p}\pi^-)}{\mathcal{B}(\Lambda_b^0 \to \Lambda_c^+ \pi^-)} = 0.0540
\pm 0.0023 \pm 0.0032. \end{equation*} Two resonant structures are observed in
the $ \Lambda_c^+ \pi^-$ mass spectrum of the ${\Lambda_b^0 \to \Lambda_c^+
p\overline{p} \pi^-}$ decays, corresponding to the $\Sigma_c(2455)^0$ and
$\Sigma_c^{*}(2520)^0$ states. The ratios of branching fractions with respect
to the decay $\Lambda_b^0 \to \Lambda_c^+ p \overline{p} \pi^-$ are
\begin{align*}
  \frac{\mathcal{B}(\Lambda_b^0 \to \Sigma_c^0
p\overline{p})\times\mathcal{B}(\Sigma_c^0\to \Lambda_c^+
\pi^-)}{\mathcal{B}(\Lambda_b^0 \to \Lambda_c^+ p \overline{p}\pi^-)} =
0.089\pm0.015\pm0.006,
  \frac{\mathcal{B}(\Lambda_b^0 \to \Sigma_c^{*0}
p\overline{p})\times\mathcal{B}(\Sigma_c^{*0}\to \Lambda_c^+
\pi^-)}{\mathcal{B}(\Lambda_b^0 \to \Lambda_c^+ p \overline{p}\pi^-)} =
0.119\pm0.020\pm0.014. \end{align*} In all of the above results, the first
uncertainty is statistical and the second is systematic. The phase space is
also examined for the presence of dibaryon resonances. No evidence for such
resonances is found.
