A new page in the history of the United States labor movement was written here today.

United Auto Workers President Douglas A. Fraser became the first major union leader to join the board of an important American company when Chrysler Corp. shareholders overwhelmingly elected him -- and 19 other management nominees -- to be a director of the financially troubled automaker.

Fraser's election is a trade-off for the union's decision to grant Chrysler more than $460 million in concessions to help keep the company afloat.

The move is controversial. Few union leaders and fewer corporations want union representation on boards of directors, a common practice in many European countries. Unions worry that worker-directors will become ineffective bargainers.

Corporate executives say that union directors may have interests that conflict with the good of the company and also are fearful of giving confidential corporate data to a union leader who bargains with their competitors, as well.

Fraser, at a morning briefing, countered that "workers have more at stake" is the survival of Chrysler than anyone else, including shareholders and management.

Chrysler's survival is in serious jeopardy. The federal government last week granted the company $1.5 billion in loan guarantees, and banks, local governments, Canada, suppliers and dealers -- as well as the UAW -- have chipped in another $2 billion. But Chrysler Chairman Lee A. Iacocca conceded to shareholders today that the company is "not out of the woods yet."

In Detroit, meanwhile, Chrysler announced yesterday it would give rebates for certain 1979 and 1980 models for purchases through June 20, news services reported.

The released on 1979 models range from $200 to $1,000 (on four-wheel drive Dodge pickups and Ramchargers and the Plymouth Trailduster), while the paybacks on selected 1980 models are to be $300 or $500.

An earlier Chrysler rebate program expired on April 30.

The company lost nearly $1.1 billion last year -- a record for an American company and lost another $449 million during the first three months of 1980.

Iacocca said the automaker hopes to "start taking down the loan guarantees by about the end of this month."

Chrysler needs funds, it says, to enable it to get through the next four or five months when it will introduce a new set of four-wheel-drive, fuel-efficient compact cars and increase its ability to make its successful Omni and Horizon subcompacts. Fraser told reporters this morning that the company was days away from running out of cash.

The severe depression in the entire auto industry -- which began with the advent of gasoline lines last spring and worsened when the recession and high interest rates struck last February -- makes Chrysler's plight even worse.

The company has sold off divisions and subsidiaries, closed old plants, changed marketing and production techniques, replace management and redesigned many of its products to become competitive again.

Iacocca emphasized to shareholders today that there is a "new Chrysler Corp.," and the old one that tried to do the same thing that its bigger and better-heeled competitors General Motors and Ford tried to do. Until 1978 Chrysler was the 10th-biggest corporation in the United States.

Fraser told reporters that the restructured company can survive, although the one in existence a year ago could not have. But the company will be smaller, he said, employing perhaps 100,000 UAW members, compared with 130,000 a year ago. Today, because of layoffs, only about 73,000 workers are on the job at Chrysler, and throughout the auto industry about 25,000 workers are collecting unemployment.

Because of the sharp rise in demand for small cars, Japanese producers have rushed in to sell cars Detroit cannot yet make in sufficient quantity. Both Fraser and Iacocca have called for restraints on Japanese production, suggesting that Japan stop working overtime to ship vehicles to the United States.

"This wouldn't cause the layoff of a single Japanese worker; it wouldn't require a tariff; it wouldn't start a trade war. It would reduce exports by about 300,000 to 400,000 units a year simply because Japanese automakers wouldn't be working around the clock and on weekends while Americans remain unemployed," Iacocca said.

Although Chrysler's future remains bleak and the company will pay no dividends for some time to come, Iacocca received mostly praise and little criticism from the several hundred shareholders who ventured to this industrial town about 80 miles northwest of Chicago.

One shareholder criticized Iacocca for holding the meeting "in the sticks." The gathering was held a few miles from Chrysler's most efficient plant, in Belvidere, Ill., which turns out Omnis and Horizons.

Despite the controversy surrounding Fraser's election to the board, there was little discussion of the step at the meeting today and the UAW president received all but about 1 percent of the more than 44.5 million ballots cast.

One shareholder predicted that by putting a labor leader on its board of directors, Chrysler is saying "goodbye to dividends. It's a very, very sad day."

One union member, who is also a stockholder, charged that Fraser was violating the UAW constitution and questioned whether he "could serve two masters."

Iacocca, who was ousted as president of Ford Motor Co. in 1978 and came to Chrysler the same year, lauded Fraser.

"He knows this business inside and out, not only what is needed to design and build quality products, but also what is needed to keep a company in tune with the larger problems facing this industry and this country."

Fraser has said he will not participate in board decisions that affect collective bargaining. "As a result, I see no conflict of interest in his serving on the board," Iacocca said.