The decision by the Chrysler Corp. to give the United Auto Workers union a seat on the company's board of directors marks a potentially revolutionary change in U.S. labor relations.

Few unions are apt to rush out and try to follow the UAW's example. Chrysler granted the union a seat on its board only after the UAW gave it $403 million in financial aid -- putting UAW in a position few other unions are in or want to be in.

But the UAW experiment with "codetermination" -- worker representation on corporate boards -- is bound to serve as a testing ground for the future.

The most immediate question arising from the Chrysler decision is what will happen to the traditional adversary relationship between labor and management if labor allows itself to become part of management.

"nothing," a UAW official insisted yesterday. "We'll still have an adversary relationship."

But now, union officals insist, the UAW will have a relationship that includes giving "workers a voice at the highest levels of policymaking." And, the union notes, "with only one vote out of 17 on the Chrysler board, the power is ultimately with the 125,000 members" working for Chrysler.

Critics of the Chrysler decision -- mostly academics -- express concern that the union will be co-opted by having representation on the board. Again the union does not seem worried.

"Worker participation is not a new concept with us," a UAW official said yesterday. "Obviously, having representation on the board does not alter the balance of power. But it does expand our influence within the company and it gives us input into company decisions."

As an example of how the union's new position with the company might help in the future, UAW officials point to Chrysler's recent decision to close down it Hamtramck assembly plant in Detroit.

"We only found out about the closing an hour before the company announced it," a UAW official said. If we had been on the board we would have known about it and possibly been able to make a case for keeping it open."

For the UAW, traditionally one of the nation's most progressive unions, such talk makes sense and sounds reasonalble.

Outside the auto industry, however, co-determination is still viewed with skepticism. An Associated Press survey yesterday of the nation's key union leaders showed little interest in winning representation on the boards of the corporations they deal with.

"I may be a little old-fashioned, but I believe management should manage and unions should negotiate contracts," said George Hutchins, secretary-treasurer of the International Union of Electrical Workers. And George Puolin, vice president of the International Association of Machinists, also opposed the move. "The adversary system we have now has worked rather well to date . . . I don't think you can wear two hats," he said.

For many people, however, a bigger and unspoken concern is the belief that the action taken by Chrysler and the UAW is simply the first step toward socialsim.

Co-determination is basically the product of European social democrats. Yet in nations such as Sweden and West Germany, where socialism is an accepted fact, co-determination is still in the experimental stage. The idea that co-determination is now a reality in one of the largest corporations in the United States is hard for some to accept.

As foreign as the idea of co-determination might seem to them, however, it is a logical next step in the evolutions of U.S. labor relations.

During the 1970s the nation's manufacturing industries and their unions have been working closer and closer to solve mutual problems. Perhaps nowhere has this been more evident than in the auto industry.

Throughout the decade the UAW has generally been one of the industry's closest allies when it came to lobbying Congress for changes in trade legislation or modifications in environmental and fuel-efficiency standards.

The United Steelworkers union and the nation's steel industry have also successfully lobbied together, for quotas on imported steel.

After a decade of this type of cooperation, co-determination appears headed for more testing as labor relation's philosphy of the 1980s.