The prompt production of the charmonium chi(c1) and chi(c2) mesons has been studied in proton-proton collisions at the Large Hadron Collider at a centre-of-mass energy of root s = 7 TeV. The chi(c) mesons are identified through their decays chi(c) -> J/psi gamma with J/psi -> mu(+)mu(-) using 36 pb(-1) of data collected by the LHCb detector in 2010. The ratio of the prompt production cross-sections for the two chi(c) spin states. sigma(chi(c2))/sigma(chi(c1)), has been determined as a function of the J/psi transverse momentum, p(T)(J/psi), in the range from 2 to 15 GeV/c. The results are in agreement with the next-to-leading order non-relativistic QCD model at high p(T)(J/psi) and lie consistently above the pure leading-order colour-singlet prediction. (C) 2012 CERN. Published by Elsevier B.V. All rights reserved.