Premier is not one of the world's biggest oil companies. It has oil reserves of just 195 million barrels, a fraction of the 4.7 billion barrels held by BP.
It is not deterred by the so-called Helms-Burton law that bars US companies from trading with those who took over $1.8bn (pounds 1.2bn) of assets in Cuba formerly owned by the likes of Coca-Cola, Texaco and Colgate-Palmolive.
The potential oil fields Premier is exploring simply aren't the same kind of assets. "We are on very solid legal ground," said Richard Haythornthwaite, board director with Premier, in charge of exploration.
Cuba itself would be delighted if Premier's exploration proves successful. Cuba needs oil badly. It has struggled since its oil supplies dried up when the Cold War ended in 1989.
Lacking the patronage it built with the Soviet Union over three decades, Cuba's economy shrank 35 per cent in the following four years. Blackouts became routine, the US tightened its economic embargo through the Helms- Burton act, and predicting the downfall of President Castro became fashionable.
Now, a handful of oil companies led by Premier Oil and Canada's Sherritt International are spearheading a push to find huge petroleum deposits in the resource-poor Caribbean nation, a move that if successful would prove embarrassing to the US, and stoke tensions with the European Union.
"Finding oil would be like Christmas for Cuba," said Tony Kapcia, an expert on Cuba's modern history at the University of Wolverhampton. "Almost the last thing the US government wants at any stage is for Fidel Castro to survive yet another president's term and then to find oil on top of that."
In the next few weeks, London-based Premier is expected to go ahead with plans to drill a new well to probe for oil reserves under Cuba's land mass, company officials say.
Acknowledging the prospect is a long-shot, with odds of success of perhaps 20 to 1, Premier said it has identified underground rock structures that might contain between 500 million and a billion barrels of oil - a world- class find. "It is massive," said Mr Haythornthwaite. "If this comes in, Premier would be a fundamentally different company and Cuba would be a fundamentally different country."
The odds are against success. Cuba's last oil discovery in 1995 tapped oil so heavy it more resembled boot polish than fuels like the diesel and gasoline derived from crude petroleum. Major oil companies have looked at the nation's prospects and walked away.
"On the basis of the geology we've seen there's nothing we'd go for down there," said Rodney Chase, BP managing director in charge of oil exploration and production. "That doesn't mean there isn't opportunity for someone else."
Even so, Premier isn't alone in its interest in Cuba. Sherritt picked up more exploration turf in January from Talisman Energy even after Talisman lost $18m drilling there. It is also drilling a number of exploration wells, though its officials didn't return repeated telephone calls seeking a comment.
At Premier, executives are chasing a new geological theory with new drilling technology. Using data gathered by seismic tests, which use sound waves to chart underground rock structures, Premier believes it can identify previously unseen reservoirs beneath a layer of volcanic rock.
Years ago, rocks formed by volcanoes or super-heated salt sheets scattered seismic waves, preventing accurate mapping of what lies below. Now, though, Premier and others from the Royal Dutch/Shell Group to Anadarko Petroleum Corp are using computer technology made by the likes of Sun Microsystems to refine seismic images bounced off such rocks into something that can be interpreted.
That technology, referred to as a 3-D seismic, has revolutionised the search for oil and breathed new life into regions such as the Gulf of Mexico, where majors such as Shell and BP have made major finds.
"A couple of bright guys can come up with something everybody else has overlooked," said Bob Sprague, exploration director for Shell in Europe, adding that his company hasn't identified anything of interest in Cuba.
At Premier, Mr Haythornthwaite said the company is reviewing seismic data it gathered and is likely to approve a new drilling project in the next few weeks. The well would be cheap by industry standards - about $7m compared to the roughly $30m BP and Amoco spent for their wells tapping giant oil and gas reservoirs in Colombia.
Even he admits the well Premier would drill is apt to be dry. The potential rewards justify the risk, though.
"We see a formation, but we do not know if any oil is there," Mr Haythornthwaite said. "It has the potential to be one of the world's great remaining oil plays, and there's not a lot of them left in the world."
What makes this prospect so tasty is the proximity of the wells to the consumer. On its own, Cuba produces about 30,000 barrels of oil a day, about 10 per cent of what its own refineries consume, according to the Oil & Gas Journal.
Cuba needs the hard currency that's easily generated by oil sales because the US embargo blocks so many avenues to raising cash through other means. Its foreign debt has soared to $12bn last year from $8.7bn in 1993, the year after the Helms-Burton act passed.
More than a simple cash top-up, though, domestic oil supplies would give Cuba and its economy a level of stability the US has worked since 1959 to discourage, hoping Fidel Castro would fall from power. And to opponents of the current policy, it would be more evidence the US stance should change.
"If Cuba were to become self- sufficient in oil it would mean that US policy had failed," said Wayne Smith, who was an official at the US embassy in Havana until 1961 and now is an expert on the nation at the Center for International Policy, a Washington think tank. "The US interest in Cuba is the same as it is across Latin America: we don't want floods of boat people coming into the US. How does a policy that increases economic distress advance that aim? It doesn't."
The oil companies themselves are conscious of their role in the West's post Cold War policy towards former Soviet pawns. Charles Jamieson, chief executive of Premier, counts himself among a growing group of executives who believe doing business in rogue nations such as Cuba, Libya, Sudan and Iran is the best way to urge an electorate towards democracy.
"We believe that engaging these countries is better than not speaking to them," Mr Jamieson said. "We can be in these countries and make a difference."