Ascidian embryos highlight the importance of cell lineages in animal development. As simple proto-vertebrates, they also provide insights into the evolutionary origins of cell types such as cranial placodes and neural crest cells. Here we have determined single-cell transcriptomes for more than 90,000 cells that span the entirety of development-from the onset of gastrulation to swimming tadpoles-in Ciona intestinalis. Owing to the small numbers of cells in ascidian embryos, this represents an average of over 12-fold coverage for every cell at every stage of development. We used single-cell transcriptome trajectories to construct virtual cell-lineage maps and provisional gene networks for 41 neural subtypes that comprise the larval nervous system. We summarize several applications of these datasets, including annotating the synaptome of swimming tadpoles and tracing the evolutionary origin of cell types such as the vertebrate telencephalon.