Although droplet evaporation is widely assumed to be a diffusion process, our results show that when a droplet evaporates sufficiently fast it exhibits a vigorous interior flow. This flow is driven by surface tension gradients. The typical interior flow field behavior is shown as well as measurements of the droplet surface area and volume as it evaporates. We also discuss the droplet lifetime and how the system tends toward a state of marginal stability. \textcopyright{} 1996 The American Physical Society.