A search for excited states of the B-c(+/-) meson is performed using 4.9 fb(-1) of 7 TeV and 19.2 fb(-1) of 8 TeV pp collision data collected by the ATLAS experiment at the LHC. A new state is observed through its hadronic transition to the ground state, with the latter detected in the decayB(c)(+/-) -> J/psi pi(+/-). The state appears in the m(B-c(+/-)pi(+)pi(-)) - m(B-c(+/-)) - 2m(pi(+/-)) mass difference distribution with a significance of 5.2 standard deviations. The mass of the observed state is 6842 +/- 4 +/- 5 MeV, where the first error is statistical and the second is systematic. The mass and decay of this state are consistent with expectations for the second S-wave state of the B-c(+/-) meson, B-c(+/-)(2S).