  The first observation of the $\Lambda_b^0\to D_s^- p$ decay is presented
using proton-proton collision data collected by the LHCb experiment at a
centre-of-mass energy of ${\sqrt{s}=13 \,\textrm{TeV}}$, corresponding to a
total integrated luminosity of $6\,\textrm{fb}^{-1}$. Using the
$\Lambda_b^0\to\Lambda_c^+\pi^-$ decay as the normalisation mode, the branching
fraction of the $\Lambda_b^0\to D_s^- p$ decay is measured to be
${\mathcal{B}(\Lambda_b^0\to D_s^- p)=(12.6 \pm 0.5 \pm 0.3 \pm 1.2 )\times
10^{-6}}$, where the first uncertainty is statistical, the second systematic
and the third due to uncertainties in the branching fractions of the
$\Lambda_b^0\to\Lambda_c^+\pi^-$, $D_s^- \to K^-K^+\pi^-$ and $\Lambda_c^+\to p
K^- \pi^+$ decays.
