A baryonic decay of the $B_c^+$ meson, $B_c^+to J/psi poverline{p}pi^+$, is observed for the first time, with a significance of $7.3$ standard deviations, in $pp$ collision data collected with the LHCb detector and corresponding to an integrated luminosity of $3.0$ fb$^{-1}$ taken at center-of-mass energies of $7$ and $8$ $mathrm{TeV}$. With the $B_c^+to J/psi pi^+$ decay as normalization channel, the ratio of branching fractions is measured to be begin{equation*} frac{mathcal{B}(B_c^+to J/psi poverline{p}pi^+)}{mathcal{B}(B_c^+to J/psi pi^+)} = 0.143^{,+,0.039}_{,-,0.034},(mathrm{stat})pm0.013,(mathrm{syst}). end{equation*} The mass of the $B_c^+$ meson is determined as $M(B_c^+)=6274.0pm1.8,(mathrm{stat})pm0.4,(mathrm{syst}),mathrm{MeV}/c^2$, using the $B_c^+to J/psi poverline{p}pi^+$ channel.
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