The energy dependence of the relative production rate of three-jet events is studied in hadronic e+e− annihilation events at center of mass energies between 22 and 46.7 GeV. Three-jet events are defined by a jet finding algorithm which is closely related to the definition of resolvable jets used in O(αs2) perturbative QCD calculations, where the relative production rate of three-jet events is roughly proportional to the size of the strong coupling strength. The production rates of three-jet events in the data decrease significantly with increasing centre of mass energy. The experimental rates, which are independent of fragmentation model calculations, can be directly compared to theoretically calculated jet production rates and are in good agreement with the QCD expectations of a running coupling strength. The hypothesis of an energy independent coupling constant can be excluded with a significance of four standard derivations.