The prompt production of charmonium chi(c) and J/psi states is studied in proton-proton collisions at a centre-of-mass energy of root s = 7 TeV at the Large Hadron Collider. The chi(c) and J/psi mesons are identified through their decays chi(c) -> J/psi gamma and 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 chi(c) and J/psi, sigma(chi(c) -> J/psi gamma)/sigma(J/psi). is determined as a function of the J/psi, transverse momentum in the range 2 < P-T(J/psi) < 15 GeV/c. The results are in excellent agreement with next-to-leading order non-relativistic expectations and show a significant discrepancy compared with the colour singlet model prediction at leading order, especially in the low P-T(J/psi) region. (C) 2012 CERN. Published by Elsevier B.V. All rights reserved.