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).