Abstract: A study of B-c(+) -> 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 13TeV, corresponding to an integrated luminosity of 9 fb(-1). The decay B-c(+) -> 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/psi pi(+) decay is measured to be BBc+ ->chi c2 pi+/BBc+ -> (J/psi pi+) = 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 chi(c2) -> J/psi gamma branching fraction. No significant B-c(+) -> chi(+)(c1 pi) signal is observed and an upper limit for the relative branching fraction for the B-c(+) -> chi(c1)pi(+) and B-c(+) -> chi(c2)pi(+) decays of BBc+ ->chi c1 pi+/BBc+ -> chi(c2)pi(+) < 0.49 is set at the 90% confidence level.