High-throughput mapping of cellular differentiation hierarchies from single-cell data promises to empower systematic interrogations of vertebrate development and disease. Here we applied single-cell RNA sequencing to >92,000 cells from zebrafish embryos during the first day of development. Using a graph-based approach, we mapped a cell-state landscape that describes axis patterning, germ layer formation, and organogenesis. We tested how clonally related cells traverse this landscape by developing a transposon-based barcoding approach (TracerSeq) for reconstructing single-cell lineage histories. Clonally related cells were often restricted by the state landscape, including a case in which two independent lineages converge on similar fates. Cell fates remained restricted to this landscape in embryos lacking the chordin gene. We provide web-based resources for further analysis of the single-cell data.