The cranial neural crest generates a huge diversity of derivatives, including the bulk of connective and skeletal tissues of the vertebrate head. How neural crest cells acquire such extraordinary lineage potential remains unresolved. By integrating single-cell transcriptome and chromatin accessibility profiles of cranial neural crest-derived cells across the zebrafish lifetime, we observe progressive and region-specific establishment of enhancer accessibility for distinct fates. Neural crest-derived cells rapidly diversify into specialized progenitors, including multipotent skeletal progenitors, stromal cells with a regenerative signature, fibroblasts with a unique metabolic signature linked to skeletal integrity, and gill-specific progenitors generating cell types for respiration. By retrogradely mapping the emergence of lineage-specific chromatin accessibility, we identify a wealth of candidate lineage-priming factors, including a Gata3 regulatory circuit for respiratory cell fates. Rather than multilineage potential being established during cranial neural crest specification, our findings support progressive and region-specific chromatin remodeling underlying acquisition of diverse potential.