In 1971, Manfred Eigen introduced the quasispecies equations as a way to model the evolution of single-stranded RNA molecules. In this talk, we present an extension of the quasispecies model to account for the semiconservative nature of DNA replication, whereby each strand serves as the template for the synthesis of its complementary daughter strand. This is a necessary first step toward making the quasispecies model a quantitative tool for analyzing the evolutionary dynamics of unicellular organisms. From the semiconservative quasispecies equations we are able to show that, at sufficiently high error rates, faster replicating cells die more quickly than slower replicating cells. Thus, our model provides a mathematical basis for the efficacy of chemotherapeutic agents in treating cancers.