Using $pp$ collision data corresponding to an integrated luminosity of $8.5,mathrm{fb}^{-1}$ recorded by the LHCb experiment at centre-of-mass energies of $sqrt{s} = 7$, $8$ and $13mathrm{,Tekern -0.1em V}$, the observation of an excited $B_c^+$ state in the $B_c^+pi^+pi^-$ invariant-mass spectrum is reported. The observed peak has a mass of $6841.2 pm 0.6 {,rm (stat),} pm 0.1 {,rm (syst),} pm 0.8,(B_c^+) mathrm{,MeV}/c^2$, where the last uncertainty is due to the limited knowledge of the $B_c^+$ mass. It is consistent with expectations of the $B_c^{*}(2^{3}S_{1})^+$ state reconstructed without the low-energy photon from the $B_c^{*}(1^{3}S_{1})^+ to B_c^+ gamma$ decay following $B_c^{*}(2^{3}S_{1})^+ to B_c^{*}(1^{3}S_{1})^+ pi^+ pi^-$. A second state is seen with a global (local) statistical significance of $2.2,sigma$ ($3.2,sigma$) and a mass of $6872.1 pm 1.3 {,rm (stat),} pm 0.1 {,rm (syst),} pm 0.8,(B_c^+) mathrm{,MeV}/c^2$, and is consistent with the $B_c(2^{1}S_{0})^+$ state. These mass measurements are the most precise to date.
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