Chancellor Helmut Kohl's center-right coalition today narrowly won a key state election seen as a dress rehearsal for nationwide parliamentary elections next January.

The victory in the northern farm state of Lower Saxony provided a much-needed boost for Kohl following a series of political setbacks. The 56-year-old chancellor had staked his personal prestige on the outcome of the election by playing a prominent part in the campaign despite the reported reservations of some members of his own Christian Democrat Party.

The Christian Democrats lost their overall majority in the Lower Saxony State Assembly, as nearly 6 percent of the voters swung toward the opposition Social Democrats since the last elections, in 1982. But Kohl's party managed to maintain its hold on power in the state because of an unexpectedly strong performance by their junior coalition partners, the Free Democrats, and the failure of the Greens to pick up a significant number of votes.

The opposition Social Democrats and the Greens, who favor dismantling West Germany's 19 nuclear power plants, sought to exploit public concern over the safety of nuclear power following the Chernobyl disaster. Lower Saxony derives most of its energy from nuclear power stations. The region was exposed to some of the highest radioactivity readings in West Germany because of fallout from the damaged Soviet plant.

But political commentators here said that the nuclear issue was effectively counterbalanced in voters' minds by right-wing warnings about the dangers of a "red-green" coalition. The Greens also have called for West Germany's departure from the North Atlantic Treaty Organization and the withdrawal of U.S. Cruise and Pershing missiles from West German soil, an issue that has split the Social Democrats.

It was the second time in less than a month that West European voters have defied opinion polls estimating a sharp increase in support for antinuclear groups in the wake of the Chernobyl disaster. On May 21, the Dutch electorate handed an unexpected victory to the center-right government of Prime Minister Ruud Lubbers despite the impact of Chernobyl and massive street demonstrations against the deployment of U.S. missiles.

"The outcome is of immense importance in national terms. It shows there is no chance of the SPD Social Democrats winning an outright majority in January, and there is no majority support for an SPD-Green alliance," Kohl said after today's vote.

Johannes Rau, the Social Democrat who is expected to challenge Kohl for the chancellorship next year, called the result an "outstanding success" for his party, adding that it reinforced a steady loss of support for the Christian Democrats.

Final election figures released by Lower Saxony's election office showed the Christian Democrats with 44.3 percent of the vote compared to 42.1 percent for the Social Democrats, 7.1 percent for the Greens, and 6 percent for the Free Democrats. At the last state election, the Christian Democrats won 50.7 percent, the Social Democrats 36.5 percent, the Greens 6.5 percent, and the Free Democrats 5.9 percent.

Public opinion polls taken over the last few weeks had predicted that the Greens could win as much as 10 percent of the vote and that the Free Democrats would fail to cross the minimum 5 percent threshold for representation in the Assembly.

Much of the interest in the Lower Saxony election derived from fact that its electorate of 5.6 million offers a political microcosm of West Germany as a whole. It therefore provides a more accurate forecast of what could happen in parliamentary elections next January 25 than the remaining state elections in either left-leaning Hamburg or conservative Bavaria this fall.

Ernst Albrecht, 55, the Christian Democrat prime minister of Lower Saxony, said that the center-right coalition would have won a "big majority" if today's result was repeated on a federal level. He added that fears of the opposition being swept to power on a wave of antinuclear sentiment had not been realized.

"It was tight, but we clearly made it," he told reporters.

While conceding that they were disappointed not to have ousted the Christian Democrats from power, Social Democrat officials also expressed delight with their gains.

Today's result means that the center-right coalition will retain its present majority in the Bundesrat, or upper house of the German parliament, which is made up of representatives of state governments. A defeat in Lower Saxony would have enabled the opposition to delay and possibly block important legislation.

Kohl managed to take some of the heat out of the nuclear issue by announcing the appointment of a special Ministry for the Environment, Nature Conservation, and Reactor Safety only 10 days ago. The move was seen as a direct response to public anxiety about Chernobyl, which was probably greater here than anywhere else in Western Europe.

Political analysts here said that the result should strengthen Kohl's position within his own party following internal grumblings about his leadership. Barring dramatic upsets between now and next January, it seems likely that he will lead the Christian Democrats into the next election despite a widespread reputation for political clumsiness.

Kohl's political future appeared in jeopardy earlier this year after two public prosecutors opened inquiries into allegations that he had lied to parliamentary committees investigating abuses in campaign financing. But the inquiries were dropped last month after investigators announced that they had insufficient evidence to press charges.