Artificial intelligence’s integration into everyday life has stirred up doubts and unsettling questions for many about humanity’s path forward. But in Anguilla, a tiny Caribbean island to the east of Puerto Rico, the A.I. boom has made the country a fortune.

The British territory collects a fee from every registration for internet addresses that end in “.ai,” which happens to be the domain name assigned to the island, like “.fr” for France and “.jp” for Japan. With companies wanting internet addresses that communicate they are at the forefront of the A.I. boom — like Elon Musk’s X.ai website for his artificial intelligence company — Anguilla has recently received a huge influx in requests for domain names.