The inclusive production of D*+/-(2010) mesons in deep-inelastic scattering is studied with the HI detector at HERA. In the kinematic region 1 < Q(2) < 100 GeV2 and 0.05 < y < 0.7 an e(+) p cross section for inclusive D*+/- meson production of 8.50 +/- 0.42(stat.)(-100)(+1.21)(syst.) nb is measured in the visible range p(tD*) > 1.5 GeV and eta(D*) < 1.5. Single and double differential inclusive D*+/- meson cross sections are compared to perturbative QCD calculations in two different evolution schemes, The charm contribution to the proton structure, F-c(2)(x, Q(2)), is determined by extrapolating the visible charm cross section to the full phase space. This contribution is found to rise from about 10% at Q(2) = 1.5 GeV2 to more than 25% at Q(2) = 60 GeV2 corresponding to x values ranging from 5 x 10(-5) to 3 x 10(-3). (C) 2002 Elsevier Science B.V. All rights reserved.