The Cabibbo-suppressed decay $ {\Lambda}_{\mathrm{b}}^0 $→ χ$_{c1}$pπ$^{−}$ is observed for the first time using data from proton-proton collisions corresponding to an integrated luminosity of 6 fb$^{−1}$, collected with the LHCb detector at a centre-of-mass energy of 13 TeV. Evidence for the $ {\Lambda}_{\mathrm{b}}^0 $→ χ$_{c2}$pπ$^{−}$ decay is also found. Using the $ {\Lambda}_{\mathrm{b}}^0 $→ χ$_{c1}$pK$^{−}$ decay as normalisation channel, the ratios of branching fractions are measured to be$ {\displaystyle \begin{array}{c}\frac{\mathcal{B}\left({\Lambda}_{\mathrm{b}}^0\to {\upchi}_{\mathrm{c}1}{\mathrm{p}\uppi}^{-}\right)}{\mathcal{B}\left({\Lambda}_{\mathrm{b}}^0\to {\upchi}_{\mathrm{c}1}{\mathrm{p}\mathrm{K}}^{-}\right)}=\left(6.59\pm 1.01\pm 0.22\right)\times {10}^{-2}, {}\frac{\mathcal{B}\left({\Lambda}_{\mathrm{b}}^0\to {\upchi}_{\mathrm{c}2}{\mathrm{p}\uppi}^{-}\right)}{\mathcal{B}\left({\Lambda}_{\mathrm{b}}^0\to {\upchi}_{\mathrm{c}1}{\mathrm{p}\uppi}^{-}\right)}=0.95\pm 0.30\pm 0.04\pm 0.04, {}\frac{\mathcal{B}\left({\Lambda}_{\mathrm{b}}^0\to {\upchi}_{\mathrm{c}2}{\mathrm{p}\mathrm{K}}^{-}\right)}{\mathcal{B}\left({\Lambda}_{\mathrm{b}}^0\to {\upchi}_{\mathrm{c}1}{\mathrm{p}\mathrm{K}}^{-}\right)}=1.06\pm 0.05\pm 0.04\pm 0.04,\end{array}} $where the first uncertainty is statistical, the second is systematic and the third is due to the uncertainties in the branching fractions of χ$_{c1,2}$→ J/ψγ decays.[graphic not available: see fulltext]