Abstract: The production of the eta(c)(1S) state in protonproton collisions is probed via its decay to the p (p) over bar final state with the LHCb detector, in the rapidity range 2.0 < y < 4.5 and in the meson transverse-momentum range p(T) > 6.5GeV/c. The cross-section for prompt production of eta(c)(1S) mesons relative to the prompt J/psi cross-section is measured, for the first time, to be s sigma(eta c(1S))/sigma J/psi = 1.74 +/- 0.29 +/- 0.28 +/- 0.18(B) at a centre-of-mass energy root s = 7 TeV using data corresponding to an integrated luminosity of 0.7 fb(-1), and s sigma(eta c(1S))/sigma(J/psi) = 1.60 +/- 0.29 +/- 0.25 +/- 0.17(B) at root s = 8 TeV using 2.0 fb(-1). The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the (eta c)(1S) and J/psi decays to the p (p) over bar final state. In addition, the inclusive branching fraction of b-hadron decays into (eta c)(1S) mesons is measured, for the first time, to be B(b -> X-eta c) = (4.88 +/- 0.64 +/- 0.29 +/- 0.67(B)) x10(-3), where the third uncertainty includes also the uncertainty on the J/psi inclusive branching fraction from b-hadron decays. The difference between the J/psi and (eta c)(1S) meson masses is determined to be 114.7 +/- 1.5 +/- 0.1MeV/c(2).