It is believed that all present-day organisms descended from a common cellular ancestor. Such a cell must have evolved from more primitive and simpler precursors, but neither their organization nor the route such evolution took are accessible to the molecular techniques available today. We propose a mechanism, based on functional properties of enzymes and the kinetics of growth, which allows us to reconstruct the general course of early enzyme evolution. A precursor cell containing very few multifunctional enzymes with low catalytic activities is shown to lead inevitably to descendants with a large number of differentiated monofunctional enzymes with high turnover numbers. Mutation and natural selection for faster growth are shown to be the only conditions necessary for such a change to have occurred.