The prompt and non-prompt production cross-sections for the χc1 and χc2 charmonium states are measured in pp collisions at √s = 7 TeV with the ATLAS detector at the LHC using 4.5 fb−1 of integrated luminosity. The χc states are reconstructed through the radiative decay χc → J/ψ γ (with J/ψ → μ+μ−) where photons are reconstructed from γ → e+e− conversions. The production rate of the χc2 state relative to the χc1 state is measured for prompt and non-prompt χc as a function of J/ψ transverse momentum. The prompt χc cross-sections are combined with existing measurements of prompt J/ψ production to derive the fraction of prompt J/ψ produced in feed-down from χc decays. The fractions of χc1 and χc2 produced in b-hadron decays are also measured.