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A study of B c + → χ c πi + decays is reported using proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13TeV, corresponding to an integrated luminosity of 9 fb -1 . The decay B c + → χ c2 π + 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 + decay is measured to be
(ßB c + → χ c2 π + ) / (ßB c + → J/ψπ + ) = 0.37 ± 0.06 ± 0.02 ± 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 c1 π + signal is observed and an upper limit for the relative branching fraction for the B c + → χ c1 π + and B c + → χ c2 π + decays of
(ßB c + →χ c1 π + ) / (ßB c + → χ c2 π +) ≤ 0.49
is set at the 90% confidence level.