Phylogenomics has revealed the existence of fast-evolving animal phyla in which the amino acid substitution rate, averaged across many proteins, is consistently higher than in other lineages. The reasons for such differences in proteome-wide evolutionary rates are still unknown, largely because only a handful of species offer within-species genomic data from which molecular evolutionary processes can be deduced. In this study, we use next-generation sequencing technologies and individual whole-transcriptome sequencing to gather extensive polymorphism sequence data sets from Ciona intestinalis. Ciona is probably the best-characterized member of the fast-evolving Urochordata group (tunicates), which was recently identified as the sister group of the slow-evolving vertebrates. We introduce and validate a maximum-likelihood framework for single-nucleotide polymorphism and genotype calling, based on high-throughput short-read typing. We report that the C. intestinalis proteome is characterized by a high level of within-species diversity, efficient purifying selection, and a substantial percentage of adaptive amino acid substitutions. We conclude that the increased rate of amino acid sequence evolution in tunicates, when compared with vertebrates, is the consequence of both a 2-6 times higher per-year mutation rate and prevalent adaptive evolution.