Crucial information on the coupling of the Higgs boson to bottom quarks is
expected from Higgs production in association with a forward tagging jet at a
future high-energy lepton-proton collider. In order to control the theoretical
uncertainties of the signal process, the impact of radiative corrections has to
be quantified. We present the full next-to-leading order QCD corrections to e-
p -> e- j H and e- p -> nu_e j H in the form of a flexible Monte-Carlo program
allowing for the calculation of cross sections and kinematic distributions
within experimentally feasible selection cuts. QCD corrections are found to be
very small for cross sections, while the shape distortion of distributions can
be as large as 20%. Residual scale uncertainties at next-to-leading order are
at the permille level.Comment: 15 pages, 14 figure