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 $Lambda_b^0to chi_{c1}(3872)pK^-$ with $chi_{c1}to J/psipi^+pi^-$ is observed for the first time. The significance of the observed signal is in excess of seven standard deviations. It is found that $(58pm15)%$ of the decays proceed via the two-body intermediate state $chi_{c1}(3872)Lambda(1520)$. The~branching fraction with respect to that of the $Lambda_brightarrowpsi(2S)p K^{-}$ 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^0tochi_{c1}(3872)pK^-}{Lambda_btopsi(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 0.2right)times 10^{-2},, end{equation*} where the first uncertainty is statistical and the second is systematic.
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