The χ(b)(nP) quarkonium states are produced in proton-proton collisions at the Large Hadron Collider at sqrt[s] = 7 TeV and recorded by the ATLAS detector. Using a data sample corresponding to an integrated luminosity of 4.4 fb(-1), these states are reconstructed through their radiative decays to Υ(1S,2S) with Υ → μ+ μ-. In addition to the mass peaks corresponding to the decay modes χ(b)(1P,2P) → Υ(1S)γ, a new structure centered at a mass of 10.530 ± 0.005(stat) ± 0.009(syst) GeV is also observed, in both the Υ(1S)γ and Υ(2S)γ decay modes. This structure is interpreted as the χ(b)(3P) system.