Which southern Pacific island is not considered a US territory or Protectorate?

The Cook Islands is the correct choice because it is a self-governing territory in free association with New Zealand and does not fall under U.S. jurisdiction or governance. While the Cook Islands maintains a relationship with New Zealand, it operates independently in most internal matters, including its own constitution and governance structures.

In contrast, Guam, Palmyra Atoll, and the Northern Mariana Islands are directly associated with the United States. Guam is an unincorporated territory, Palmyra Atoll is an unorganized territory, and the Northern Mariana Islands is a commonwealth in political union with the U.S. Each of these islands is subject to U.S. sovereignty and federal laws, making them U.S. territories or protectorates. Thus, the Cook Islands stands out as the only option that is not linked to the United States in a territorial or protectorate capacity.