Aqqaluk Lynge has a recurring nightmare: “When I’m lying awake at night, I pray we don’t find oil.” That anxiety puts Lynge, the president of Greenland’s chapter of the Inuit Circumpolar Council, a group representing indigenous people from Greenland, Canada, Alaska, and Russia, in the distinct minority of his 58,000 fellow islanders, most of whom hope that a huge oil find will ensure the success of Greenland’s independence from Denmark. Roughly 76 percent of the voters in a referendum last year wanted greater self-rule; on June 21 of this year, they got it.

But as part of that self-rule deal, Denmark will end up reducing its annual subsidy to Greenland—about $11,000 per person, representing about 60 percent of the island’s budget. Hence the high hopes for oil revenue. Some estimates, including those of the U.S. Geological Survey, suggest Greenland’s coastal waters could hold anywhere from 16 billion to 47 billion barrels of oil, or 800,000 barrels for every man, woman, and child. That would mean a staggering leap in income for Greenlanders, who until two generations ago were mostly subsistence hunters and fishermen.

With such massive potential oil reserves, Greenland is poised to achieve a geopolitical importance it hasn’t had since the invention of Risk. “We don’t want Greenland to be up for grabs,” worries Lynge. But oil has yet to actually be discovered, much less to flow, which is why Jens Frederiksen, the leader of Greenland’s Democratic Party, spearheaded the “no” campaign during last year’s referendum on self-governance. He says the government has too many pressing social needs—abysmal education levels, a crumbling public-housing stock, and massive rates of alcoholism—to reduce the Danish subsidy, especially since, even if oil is found, any revenue won’t start coming in for 15 or 20 years.