  Using proton-proton collision data, collected with the LHCb detector and
corresponding to 1.0, 2.0 and 1.9fb$^{-1}$ of integrated luminosity at the
centre-of-mass energies of 7, 8, and 13 TeV, respectively, the decay
$\Lambda_b^0\to \chi_{c1}(3872)pK^-$ with $\chi_{c1}\to J/\psi\pi^+\pi^-$ is
observed for the first time. The significance of the observed signal is in
excess of seven standard deviations. It is found that $(58\pm15)\%$ of the
decays proceed via the two-body intermediate state
$\chi_{c1}(3872)\Lambda(1520)$. The~branching fraction with respect to that of
the $\Lambda_b\rightarrow\psi(2S)p K^{-}$ decay mode, where the
$\psi(2S)$~meson is reconstructed in the $J/\psi \pi^+\pi^-$ final state, is
measured to be: \begin{equation*}
\frac{\Lambda_b^0\to\chi_{c1}(3872)pK^-}{\Lambda_b\to\psi(2S)p K^-} \times
\frac{\mathcal{B}(\chi_{c1} \to J/\psi \pi^+\pi^-)}{\mathcal{B}(\psi(2S)\to
J/\psi \pi^+\pi^-)} = \left(5.4 \pm 1.1 \pm 0.2\right)\times 10^{-2}\,,
\end{equation*} where the first uncertainty is statistical and the second is
systematic.
