THE LAST move on the Korean chessboard was by Soviet president Mikhail Gorbachev, who received South Korean President Roh Tae Woo in June and thus powerfully stirred the two Koreas to reach across the line that has divided them since World War II. They have now responded with an unprecedented high-level meeting of prime ministers opening what should become a deepening political dialogue. At its end shimmers the national dream of reuniting the one country of the four left divided by the Cold War that has withstood all attempts, political and military, even to start closing the gap.

It is axiomatic among observers of Korea that peaceful reunification can come only haltingly if at all while a Stalinist tyrant, Kim Il Sung, rules in the North and while a particular government, democratically elected but still heavily influenced by a wary anti-Communist military, rules in the South. But the aging and odious Kim is under pressure to open to the South -- from his de'tente-minded patrons in Moscow and Beijing and from the embarrassment born of his country's economic failure and international isolation. President Roh in the South, meanwhile, is buoyed by confidence arising from his country's economic achievement, its post-Olympics global prestige and its moral superiority as a society which, though imperfectly, respects the principle of choice. The partial democratization that the military has allowed in Seoul keeps the government under a sharp opposition spur on the reunification issue.

At the talks of the two prime ministers, South Korea emphasized its favored step-by-step confidence-building approach, which the North fears will erode its control. North Korea argued for early sweeping political and military accords, which the South sees as a plot to loosen its American connection. Yet though there was no agreement, there was an evident desire on both sides to move beyond the heady symbolism of the occasion and to seek out common ground.

There can be no denying the difficulty. Vietnam reunited by war. The two Chinas, though relaxed, remain far from united. Germany's reunification proceeded by a peaceful internal collapse in the East, of which there is no visible sign in North Korea. But there also can be no denying the appeal of reunification and the helpful and coordinated new support for it coming from Washington and Moscow with the ending of the Cold War.