  The first observation of the Cabibbo-suppressed decay $\Lambda_b^0\rightarrow
J/\psi p \pi^-$ is reported using a data sample of proton-proton collisions at
7 and 8 TeV, corresponding to an integrated luminosity of 3 $\rm fb^{-1}$. A
prominent signal is observed and the branching fraction relative to the decay
mode $\Lambda_b^0\rightarrow J/\psi p K^-$ is determined to be $$ \frac{{\cal
B}(\Lambda_b^0\rightarrow J/\psi p \pi^-)}{{\cal B}(\Lambda_b^0\rightarrow
J/\psi p K^-)}=0.0824\pm0.0025\:(\text{stat})\pm0.0042\:(\text{syst}). $$ A
search for direct CP violation is performed. The difference in the CP
asymmetries between these two decays is found to be $$ {\cal
A}_{CP}(\Lambda_b^0\rightarrow J/\psi p \pi^-)-{\cal
A}_{CP}(\Lambda_b^0\rightarrow J/\psi p K^-)=(+5.7\pm
2.4\:(\text{stat})\pm1.2\:(\text{syst}))\%, $$ which is compatible with CP
symmetry at the $2.2\sigma$ level.
