Final answer:
The National Archives and Records Administration (NARA), via the Information Security Oversight Office (ISOO), holds the regulatory priority over the identification, handling, and protection of Controlled Unclassified Information (CUI).
Step-by-step explanation:
The agency with regulatory priority over the identification, handling, and protections for Controlled Unclassified Information (CUI) is the National Archives and Records Administration (NARA), specifically through its Information Security Oversight Office (ISOO). The CUI program was established to create a consistent approach to handling unclassified information that requires safeguarding or dissemination controls pursuant to and consistent with laws, regulations, and government-wide policies. NARA's ISOO is tasked with overseeing the CUI program and ensuring that federal agencies properly identify and handle CUI to protect sensitive information from unauthorized disclosure.