The Soviet Union yesterday granted the Chevron Corp. exclusive rights for exploration and development of its largest newly discovered oil field, an 8,900- square-mile region near the Caspian Sea with reserves that are estimated to be 2 1/2 times greater than those of the Alaskan North Slope.

Richard Matzke, president of the Chevron subsidiary dealing with the Soviets, called the Tengiz oil field "one of the most significant oil provinces in the world." He added that its addition to the nearby Korolev field, which the San Francisco-based company is already exploring, increases the chances of Chevron becoming a major producer and distributor of the Soviet Union's vast oil resources.

But the exploration agreement, signed yesterday in a ceremony at the Soviet Embassy, stopped short of establishing a joint venture between Chevron and its Soviet partners that would actually sell oil and produce badly needed hard currency for Moscow.

"If our investigation is positive, and if both sides decide to proceed, we would hope to get on with production as quickly as possible," perhaps within 2 1/2 years, said Matzke.

Chevron has spent the past three years seeking oil sites in the Soviet Union and finally settled on Korolev, which is just eight miles from Tengiz in arid western Kazakhstan near the northeast corner of the Caspian Sea. Matzke said that field was so small and the environmental concerns so great that it made economic sense only if Tengiz was developed along with it.

As recently as two weeks ago, Chevron vice president Edward Scott put the odds on developing Korolev alone at about 50-50, but Matzke said the addition of the much larger Tengiz field greatly increased the chances of a deal. The Soviets, however, were reluctant to turn over the development of their largest new oil field to a foreign operation.

"It is so valuable that we never thought we could get it," said James H. Giffen, president of the American Trade Consortium, a group of six U.S. companies seeking deals in the Soviet Union. Chevron is the member whose oil sales would provide the hard currency to make deals profitable for the other companies.

Giffen said the trade consortium has a number of joint ventures on hold, waiting for Chevron to complete its own joint venture.

Meanwhile, IBM yesterday signed an agreement to sell 13,000 personal computers to Soviet schools with shipments set to start in September. The sale was made possible through new rules that allow the sale to the Soviet Union of more sophisticated computers. The deal could be worth as much as $25 million to IBM.