Prompt production of charmonium chi(c0), chi(c1) and chi(c2) mesons is studied using proton-proton collisions at the LHC at a centre-of-mass energy of root s = 7 TeV. The chi(c) mesons are identi fi ed through their decay to J/psi gamma, with J/psi -> mu(+)mu(-) using photons that converted in the detector. A data sample, corresponding to an integrated luminosity of 1.0 fb(-1) collected by the LHCb detector, is used to measure the relative prompt production rate of chi(c1) and chi(c2) in the rapidity range 2.0 < y < 4.5 as a function of the J/psi transverse momentum from 3 to 20 GeV/c. First evidence for chi(c0) meson production at a high-energy hadron collider is also presented.