[en] Jet rates in deep inelastic electron proton scattering are studied with the H1 detector at HERA for momentum transfers squared between 10 and 4000 GeV². It is shown that they can be quantitatively described by perturbative QCD in next to leading order making use of the parton densities of the proton and with the strong coupling constant α_s as a free parameter. The measured value, α_s(M_Z²)=0.123±0.018, is in agreement both with determinations from e⁺e^- annihilation at LEP using the same observable and with the world average. (orig.)