Varicella-zoster virus (VZV) causes chickenpox and shingles, and is found in human populations worldwide. The lack of temporal signal in the diversity of VZV makes substitution rate estimates unreliable, which is a barrier to understanding the context of its global spread. Here, we estimate rates of evolution by studying live attenuated vaccines, which evolved in 22 vaccinated patients for known periods of time, sometimes, but not always undergoing latency. We show that the attenuated virus evolves rapidly (~10^–6 substitutions/site/day), but that rates decrease dramatically when the virus undergoes latency. These data are best explained by a model in which viral populations evolve for around 13 days before becoming latent, but then undergo no replication during latency. This implies that rates of viral evolution will depend strongly on transmission patterns. Nevertheless, we show that implausibly long latency periods are required to date the most recent common ancestor of extant VZV to an "out-of-Africa" migration with humans, as has been previously suggested.