A study of $B_c^+to K^+K^-pi^+$ decays is performed for the first time using data 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. Evidence for the decay $B_c^+tochi_{c0}(to K^+K^-)pi^+$ is reported with a significance of 4.0 standard deviations, resulting in the measurement of $frac{sigma(B_c^+)}{sigma(B^+)}timesmathcal{B}(B_c^+tochi_{c0}pi^+)$ to be $(9.8^{+3.4}_{-3.0}(mathrm{stat})pm 0.8(mathrm{syst}))times 10^{-6}$. Here $mathcal{B}$ denotes a branching fraction while $sigma(B_c^+)$ and $sigma(B^+)$ are the production cross-sections for $B_c^+$ and $B^+$ mesons. An indication of $bar b c$ weak annihilation is found for the region $m(K^-pi^+)<1.834mathrm{,Gekern -0.1em V!/}c^2$, with a significance of 2.4 standard deviations.
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