This is a Phase 1/2, first-in-human, open-label, dose-escalation study designed to evaluate the safety, tolerability, and efficacy of BBP-631 administered to up to 25 adult participants diagnosed with classic congenital adrenal hyperplasia (CAH) (simple virilizing or salt-wasting, Group 1) or with classic salt-wasting CAH (Group 2) due to 21-hydroxylase deficiency (21-OHD) and who are monitored for 24 weeks post-treatment. All participants who receive BBP-631 will be followed for an additional 4.5 years for safety and efficacy in a separate long term follow up protocol (Study CAH-399). In total, all participants will be followed for at least 5 years after the date of treatment with BBP-631.