Abstract A study of B c + → χ c π + $$ {B}_c^{+}\to {\chi}_c{\pi}^{+} $$ decays is reported using proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb −1. The decay B c + → χ c 2 π + $$ {B}_c^{+}\to {\chi}_{c2}{\pi}^{+} $$ is observed for the first time, with a significance exceeding seven standard deviations. The relative branching fraction with respect to the B c + → J / ψ π + $$ {B}_c^{+}\to J/\psi {\pi}^{+} $$ decay is measured to be B B c + → χ c 2 π + B B c + → J / ψ π + = 0.37 ± 0.06 ± 0.02 ± 0.01 , $$ \frac{{\mathcal{B}}_{B_c^{+}\to {\chi}_{c2}{\pi}^{+}}}{{\mathcal{B}}_{B_c^{+}\to J/\psi {\pi}^{+}}}=0.37\pm 0.06\pm 0.02\pm 0.01, $$ where the first uncertainty is statistical, the second is systematic, and the third is due to the knowledge of the χ c2 → J/ψγ branching fraction. No significant B c + → χ c 1 π + $$ {B}_c^{+}\to {\chi}_{c1}{\pi}^{+} $$ signal is observed and an upper limit for the relative branching fraction for the B c + → χ c 1 π + $$ {B}_c^{+}\to {\chi}_{c1}{\pi}^{+} $$ and B c + → χ c 2 π + $$ {B}_c^{+}\to {\chi}_{c2}{\pi}^{+} $$ decays of B B c + → χ c 1 π + B B c + → χ c 2 π + = < 0.49 $$ \frac{{\mathcal{B}}_{B_c^{+}\to {\chi}_{c1}{\pi}^{+}}}{{\mathcal{B}}_{B_c^{+}\to {\chi}_{c2}{\pi}^{+}}}=<0.49 $$ is set at the 90% confidence level.