The prompt and non-prompt production cross-sections for the chi(c1) and chi(c2) charmonium states are measured in pp collisions at root s = 7TeV with the ATLAS detector at the LHC using 4.5 fb(-1) of integrated luminosity. The chi(c) states are reconstructed through the radiative decay chi c -> J/psi gamma ( with J/psi -> mu(+)mu(-)) where photons are reconstructed from gamma -> e(+)e(-) conversions. The production rate of the chi(c2) state relative to the chi(c1) state is measured for prompt and non-prompt chi(c) as a function of J/psi transverse momentum. The prompt chi(c) cross-sections are combined with existing measurements of prompt J/psi production to derive the fraction of prompt J/psi produced in feed-down from chi(c) decays. The fractions of chi(c1) and chi(c2) produced in b-hadron decays are also measured.