The most recent common ancestor of the entire human population following only maternal lines of decent is known as the mitochondrial Eve ($mtE$). $MtE$ almost certainly lived during the Paleolithic Era, before the advent of agriculture. Most population genetics studies dating the time $mtE$ have their origins in the Wright-Fisher model or some closely related model. In such models the total population size is specified externally rather than determined dynamically, and each individual essentially chooses its ancestor at random from the previous generation. An alternate approach which has received little attention is to model the population as the result of a Galton-Watson branching process. In this approach, each individual produces a random number of children, and hence the total population size is generated stochastically. In this talk I present an analysis of the Galton-Watson model of genetic drift. The approach enables an estimate of the time since $mtE$ and an estimate of the population size during $mtE$'s lifetime.