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.

For each domain registration, Anguilla’s government gets anywhere from $140 to thousands of dollars from website names sold at auctions, according government data. Last year, Anguilla’s government made about $32 million from those fees. That amounted to more than 10 percent of gross domestic product for the territory of almost 16,000 people and 35 square miles.

“Some people call it a windfall,” Anguilla’s premier, Ellis Webster, said. “We just call it God smiling down on us.”

Mr. Webster said the government used the money to provide free health care for citizens 70 and older, and it has committed millions of dollar to finish building a school and a vocational training center. The government has also allocated funds to improve its airport; doubled its budget for sports activities, events and facilities; and increased the budget for citizens seeking medical treatment overseas, he said.

The island, which relies heavily on tourism, had been hard hit by the pandemic’s restrictions on travel and a devastating hurricane in 2017. The .ai domain income was the boost the country needed.

“We never thought that it would have this potential,” Mr. Webster said.

Anguilla’s control of .ai dates back to the early days of the internet, when nations and territories were assigned their slice of cyberspace. Anguilla received .ai, and its government, whose own site is www.gov.ai., did not make much of it until the domain names started bringing in millions. Officials are uncertain how long the boon will last, but they predicted 2024 would bring in similar income as last year from domain names.

It is not the first bonanza to make a big difference to a grateful domain owner. Tuvalu, a string of islands northwest of Australia, sold the rights to its suffix, “.tv,” to a Canadian entrepreneur for $50 million, and used the money to put electricity on the outer islands, create scholarships and finance the process to join the United Nations.

The South Pacific island of Niue, on the other hand, gave an American businessman the rights to its “.nu” suffix in the 1990s in exchange for connecting it to the internet. The island later claimed to have been cheated out of cash that came through the sale of the domain name to thousands of Scandinavians attracted by the suffix “nu,” which means “now” in Swedish, Danish and Dutch.

But Anguilla realized early enough that it could not let this unexpected jackpot slip away.

“It’s just lucky for us,” Mr. Webster said.

Brian Hoerst contributed reporting.