The Red Queen hypothesis proposes that coevolution of interacting species (such as hosts and parasites) should drive molecular evolution through continual natural selection for adaptation and counter-adaptation. Although the divergence observed at some host-resistance and parasite-infectivity genes is consistent with this, the long time periods typically required to study coevolution have so far prevented any direct empirical test. Here we show, using experimental populations of the bacterium Pseudomonas fluorescens SBW25 and its viral parasite, phage Φ2, that the rate of molecular evolution in the phage was far higher when both bacterium and phage coevolved with each other than when phage evolved against a constant host genotype. Coevolution also resulted in far greater genetic divergence between replicate populations, which was correlated with the range of hosts that coevolved phage were able to infect. Consistent with this, the most rapidly evolving phage genes under coevolution were those involved in host infection. These results demonstrate, at both the genomic and phenotypic level, that antagonistic coevolution is a cause of rapid and divergent evolution, and is likely to be a major driver of evolutionary change within species.