Résumé : 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. Single and double differential inclusive jet cross sections are measured as a function of Q 2 and of the transverse energy E T of the jets in the Breit frame. 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 α s (M Z) is determined. The ratio of the inclusive jet cross section to the inclusive neutral current cross section is also measured and used to extract a precise value for α s (M Z) = 0.1193 ± 0.0014 (exp.) -0.0030 +0.0047 (th.) ± 0.0016 (pdf). © 2007 Elsevier B.V. All rights reserved.