The production of D-{*}+/- mesons in deep inelastic e p scattering has been measured for exchanged photon virtualities 5 < Q(2) < 1000 GeV2, using an integrated luminosity of 363 pb(-1) with the ZEUS detector at HERA. Differential cross sections have been measured and compared to next-to-leading-order QCD calculations. The cross-sections are used to extract the charm contribution to the proton structure functions, expressed in terms of the reduced charm cross section, sigma(c (c) over bar)(red). Theoretical calculations based on fits to inclusive HERA data are compared to the results.