Using proton-proton collision data, collected with the LHCb detector and corresponding to 1.0, 2.0 and 1.9fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ of integrated luminosity at the centre-of-mass energies of 7, 8, and 13 TeV, respectively, the decay $\Lambda b0\to \chi c1(3872)pK-$ 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 $(58\pm 15)\%$ of the decays proceed via the two-body intermediate state $\chi c1(3872)\Lambda (1520)$. The~branching fraction with respect to that of the $\Lambda b\to \psi (2S)pK-$ 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.