The first observation of the Cabibbo-suppressed decay $Lambda_b^0rightarrow J/psi p pi^-$ 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 $Lambda_b^0rightarrow J/psi p K^-$ is determined to be $$ frac{{cal B}(Lambda_b^0rightarrow J/psi p pi^-)}{{cal B}(Lambda_b^0rightarrow J/psi p K^-)}=0.0824pm0.0025:(text{stat})pm0.0042:(text{syst}). $$ A search for direct CP violation is performed. The difference in the CP asymmetries between these two decays is found to be $$ {cal A}_{CP}(Lambda_b^0rightarrow J/psi p pi^-)-{cal A}_{CP}(Lambda_b^0rightarrow J/psi p K^-)=(+5.7pm 2.4:(text{stat})pm1.2:(text{syst}))%, $$ which is compatible with CP symmetry at the $2.2sigma$ level.
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