The semi-inclusive reaction e+ p -> e+ X p was studied with the ZEUS detector at HERA using an integrated luminosity of 12.8 pb-1. The final-state proton, which was detected with the ZEUS leading proton spectrometer, carried a large fraction of the incoming proton energy, xL>0.32, and its transverse momentum squared satisfied pT^2<0.5 GeV^2; the exchanged photon virtuality, Q^2, was greater than 3 GeV^2 and the range of the masses of the photon-proton system was 45<W<225 GeV. The leading proton production cross section and rates are presented as a function of xL, pT^2, Q^2 and the Bjorken scaling variable, x.