A search for excited states of the Bc(±) 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 decay Bc(±)→J/ψπ(±). The state appears in the m(Bc(±)π(+)π(-))-m(Bc(±))-2m(π(±)) 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 Bc(±) meson, Bc(±)(2S).