The charged particle multiplicity distribution of hadronic Z decays was measured on the peak of the Z resonance using the ALEPH detector at LEP. Using a model independent unfolding procedure the distribution was found to have a mean <n> = 20.85 +/- 0.24 and a dispersion D = 6.34 +/- 0.12. Comparison with lower energy data supports the KNO scaling hypothesis in the energy range square-root s = 29-91.25 GeV. At square-root s = 91.25 GeV the shape of the multiplicity distribution is well described by a log-normal distribution, as predicted from a cascading model for multi-particle production. The same model also successfully describes the energy dependence of the mean and width of the multiplicity distribution. A next-to-leading order QCD prediction in the frame-work of the modified leading-log approximation and local parton-hadron duality is found to fit the energy dependence of the mean but not the width of the charged multiplicity distribution, indicating that the width of the multiplicity distribution is a sensitive probe for higher order QCD or non-perturbative effects.