A search for the decays of the $B_c^+$ meson to $pbar ppi^+$ is performed for the first time using a data sample corresponding to an integrated luminosity of 3.0 $mathrm{fb}^{-1}$ collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of $7$ and $8$ TeV. No signal is found and an upper limit, at 95% confidence level, is set, $frac{f_c}{f_u}timesmathcal{B}(B_c^+to pbar ppi^+)<3.6times10^{-8}$ in the kinematic region $m(pbar p)<2.85mathrm{,Gekern -0.1em V!/}c^2$, $p_{rm T}(B)<20mathrm{,Gekern -0.1em V!/}c$ and $2.0<y(B)<4.5$, where $mathcal{B}$ is the branching fraction and $f_c$ ($f_u$) is the fragmentation fraction of the $b$ quark into a $B_c^+$ ($B^+$) meson.