The Cabibbo-suppressed decay $\Lambda b0\to \chi c1p\pi -$ is observed for the first time using data from proton-proton collisions corresponding to an integrated luminosity of 6fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, collected with the LHCb detector at a centre-of-mass energy of 13TeV. Evidence for the $\Lambda b0\to \chi c2p\pi -$ decay is also found. Using the $\Lambda b0\to \chi c1pK-$ decay as normalisation channel, the ratios of branching fractions are measured to be $$\begin{array}{rcl} \frac{ \mathcal{B} (\Lambda_b^0\rightarrow\chi_{c1}p\pi^-)}{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c1}pK^-)} & = & (6.59 \pm 1.01 \pm 0.22 ) \times 10^{-2} ,, \frac{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c2}p\pi^-)}{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c1}p\pi^-)} & = & 0.95 \pm 0.30 \pm 0.04 \pm 0.04 ,, \frac{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c2}pK^-)}{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c1}pK^-)} & = & 1.06 \pm 0.05 \pm 0.04 \pm 0.04 ,,\end{array}$$ where the first uncertainty is statistical, the second is systematic and the third is due to the uncertainties in the branching fractions of $\chi c1,2\to J/\psi \gamma$ decays.