  Inclusive jet production is studied in neutral current deep-inelastic
positron-proton scattering at large four momentum transfer squared Q^2>150
GeV^2 with the H1 detector at HERA. The measurements are found to be well
described by calculations at next-to-leading order in perturbative QCD.
  The running of the strong coupling is demonstrated and the value of
alpha_s(M_Z) is determined.
