It is laying a link that will carry the first gush of Azerbaijan's huge off-shore oil deposits from a platform to Baku, on the Caspian's western shore. It is a delicate business, which involves negotiating a path around underwater volcanoes, cliffs and yawning chasms.
But that task is dwarfed by larger issues: the barge is also picking its way along the political equivalent of the San Andreas fault, a crack in the geopolitical crust that once separated the Ottoman, Persian and Russian empires, and now divides their modern equivalents, whose appetites are whetted anew by the whiff of oil.
No one knows how much oil lies in the Caspian basin. A recent US State Department report said there may be 178 billion barrels, more than Kuwait's 100 billion barrels. Oil executives believe that to be an exaggeration, yet few dispute that the sea conceals deposits likely to be two or three times the North Sea's. The problem is not so much getting it to the surface, although there are squabbles about how to divide up the Caspian territorially among the five nations that circle its shores. The real issue is how to get oil to market from a land-locked sea overshadowed by the planet's bully-boys, and across a mountainous region fraught by ethnic strife, banditry, and small wars.
There has already been turmoil since the scale of the Caspian's riches - the treasure Hitler sought when he invaded the Soviet Union in 1941 - began to emerge. One reason Russia sent the tanks into Chechnya in 1994, beginning a conflagration that cost 80,000 lives, was to control a pipeline that ran across Chechen turf.
Yet, undeterred, the former Soviet republic of Azerbaijan is forging ahead with extracting its share of the spoils at breakneck speed. "Five years ago I was sitting in a little office in the centre of Baku's old city, thinking what the hell would I do next," said Terry Adams, a Welshman with BP. "Now look where we are." We are sitting in his headquarters, a former Communist palace of culture decked with original oil paintings. Mr Adams is head of the Azerbaijan International Operating Company (AIOC), the leading player in a group of five consortia given oil concessions by Azerbaijan. He shows visitors a map of southern England with a long streak drawn diagonally across it, stretching from the M25's north-western edge at High Wycombe to its south- eastern rim, near Rochester. That, he explains, is the size of his field, an estimated 4 billion barrels which will be pumped out over the next 30 years. "It may be bigger," he adds. "It would be surprising if it didn't grow." The pipe-laying barge now crossing the Caspian is laying a link for his platform, the Chirag 1, which he hopes will have its first oil by August.
No one is more keenly aware than he of the historical and geopolitical significance of the events now under way, a contest often compared with the Great Game, the 19th-century struggle waged over India between the British Empire and Russia. "We are seeing a really changing geopolitical balance in the region," he remarks cautiously.
Critical to the future of his BP-led consortium, which is 40 per cent American, is the policy of Azerbaijan's president, Haidar Aliyev, a veteran of the Soviet KGB and Politburo. A close colleague of Brezhnev's, the 73-year-old president has played an artful hand, keeping predatory powers at bay by sharing out the riches and punishing troublemakers.
Any external attempt to interfere with Azerbaijan is likely to meet with opposition from 11 countries whose oil interests have a stake in the five consortia. Iran and Britain have holdings in two of them; Russia and the US have a cut in three. "Aliyev has created a situation where the West and others have been brought in on a commercial basis to form a pretty consolidated geopolitical group, which is highly motivated by commercial and self-interests," said one Baku source.
"Just look, he's got London, Washington, Paris, Brussels, Bonn, Moscow, Tbilisi, Tehran, Istanbul, and Tokyo."
For now, the mighty forces bearing down on Azerbaijan's new wealth appear to be play-ing along in the mutual pursuit of profit. But the potential for trouble still exists, not least because the routes by which Azerbaijan's oil will get to the international market have yet to be settled.
It is already agreed that the first - or "early" - Azeri oil will flow along two routes, which will operate indefinitely. One is through a Soviet-era pipe system which runs 850 miles north-west across Chechnya and on through southern Russia to the Black Sea port of Novorossisk. The Russians have pledged that the pipeline will be ready by October, even though the Chechen section is full of leaks.
The second runs 550 miles west across Georgia to a terminal to be built near Supsa. This is not expected to be ready until the end of next year.
At stake is a much larger issue - the path of the main export pipeline that will eventually be built to carry a large share of the Azeri oil, 500,000 barrels a day, to the market place in some eight years.
Next month the AIOC will present Mr Aliyev with a feasibility study outlining three main options. Up to two years of research and costing will follow, in which all the arguments about funding, pipeline security, and politics will be aired. The ultimate decision rests with President Aliyev, but he will be under pressure from all sides.
One of the report's options is a pipeline running west through Georgia and south to the Turkish Mediterranean port of Ceyhan. It has strong US support, because it would keep the oil out of Moscow's reach. The Russians favour a second option: a pipe along the same path as their existing Novorossisk route. "There's a Russian saying," said Fikret Aliyev, general director of Lukoil in Baku. "Where there is one path, another will follow." A third option, the shortest and cheapest, is another pipe to Supsa. But Georgia, though leaning Westwards, has Russian troops on its soil. The route also runs close to the border with Armenia, with which Azerbaijan is still locked in conflict over Nagorno-Karabakh. Western and Turkish pressure for a pipeline to Ceyhan - perhaps a spur, running south from Georgia - seems likely to prevail. Politics, not economics, seems certain to be the decisive factor: the Ceyhan route is by far the longest, some 1,040 miles, and runs across difficult terrain. It is therefore also the most costly.
As they jockey for position, all the region's players have resorted to using their elbows. President Bill Clinton has been cosying up to Mr Aliyev, chatting with him by phone, and inviting him to visit to Washington. Turkey is trying to tilt the balance its way by complaining of the environmental perils of sending more oil tankers from the Black Sea ports through the Bosphorus. Azerbaijan believes Iran is muddying the waters by funding new mosques in the countryside in a bid to spread Islamic fundamentalism. Despite a three-year ceasefire, there has been a flurry of fighting along the Azerbaijan-Armenian border, which runs close to the Georgian route.
The murkiest role of all has been played by Russia. Moscow's strategy has been contradictory. The Russian oil company Lukoil appears willing to work in harness with Azerbaijan and other foreign oil companies in the hope that cooperation will lead to profits all round. Moreover, the newly energised Yeltsin government is showing signs of supporting that view.
Yet champing at the bit is an uncompromising and aggressive element that has yet to come to terms with Russia's loss of imperial status, clings to the notion that Moscow can dictate policy in the Caucasus and beyond, and is particularly sickened by the spectacle of an ascendant Azerbaijan, enriched by oil that the Soviet Union failed to exploit.
"In Russia, there are some very powerful circles strongly connected to the arms lobby, whose ideology is that Russian geopolitical interests dictate the expulsion of the Western economic presence in the Caspian and the Caucasus," said Vafa Goulizade, adviser to Mr Aliyev. Azerbaijan is willing to work with Moscow, he said, so long as Russia stops making mischief. "We want to co-operate with them, but with full respect to our independence and sovereignty ... they must understand that they will never again be a totalitarian superpower." Will Russia be able to resist it? Moscow's past performance is scarcely promising.
It is strongly suspected of having a hand in two failed coups against Mr Aliyev, and of masterminding the 1995 assassination attempt against his ally in neighbouring Georgia, Eduard Shevardnadze. Azerbaijan's security services accuse Russia of training Armenian troops in southern Russia; there are reports of non-Russian ships being harassed in the Black Sea, apparently as part of a strategy to undermine the argument for a pipeline through Georgia.
At the top of Moscow's rap sheet is a piece of skulduggery that it now admits - the gift of $1bn of arms to Baku's enemies in Armenia in a breathtakingly cynical attempt to prolong divisions in the southern Caucasus. The government has handed the file over to the prosecutor, after characterising the weapons transfer, in 1994-96, as the act of renegade military officers, notably the disgraced former defence minister Pavel Grachev. Yet suspicions abound in Baku that it was official policy, which has since been abandoned. At the moment, as the pipe-laying barge glides across the Caspian, peace prevails. How long that will last is anyone's guess.
With so much at stake, from money to history itself, the Great Game seems certain to go into extra time.