Multicellular systems develop from single cells through distinct lineages. However, current lineage-tracing approaches scale poorly to whole, complex organisms. Here, we use genome editing to progressively introduce and accumulate diverse mutations in a DNA barcode over multiple rounds of cell division. The barcode, an array of clustered regularly interspaced short palindromic repeats (CRISPR)/Cas9 target sites, marks cells and enables the elucidation of lineage relationships via the patterns of mutations shared between cells. In cell culture and zebrafish, we show that rates and patterns of editing are tunable and that thousands of lineage-informative barcode alleles can be generated. By sampling hundreds of thousands of cells from individual zebrafish, we find that most cells in adult organs derive from relatively few embryonic progenitors. In future analyses, genome editing of synthetic target arrays for lineage tracing (GESTALT) can be used to generate large-scale maps of cell lineage in multicellular systems for normal development and disease.