CHRYSLER'S TROUBLES, at it teeters on the edge of bankruptcy, are drawing this country into a new and unfamiliar stage of industrial organization. At least it's umfamiliar to Americans. The Chrysler solution, as it now takes shape, begins to look much like patterns that Western Europe has used for years. One question is whether European ideas can be translated successfully into American practice. Another is whether Chrysler can carry the weight of the political commitments and ideological baggage that this bail-out threatens to load onto it.

There's not much doubt that in a week or so the Carter administration will announce support for some sort of loan guarantee. Congress will probably cooperate -- although perhaps with additional conditions of its own. It that all happens on schedule, by the turn of the year there will be a new office in the Treasury Department to keep a sharp eye on Chrysler's management.

It's going to be a highly participatory corporation, since it will have not only the Treasury looking over its shoulder but also the United Auto Workers in its boardroom. To persuade the union not to press immediately for higher wages, Chrysler has agreed to put the union's president, Douglas Fraser, on its board of directors. Union representation on corporate boards has been the practice in West Germany for nearly three decades. But that does not necessarily make it any easier for an endangered company to balance responsibilities to shareholders with responsibilities to employees.

The mayor of Detroit, Coleman Young, was here last week testifying forcefully in behalf of aid for Chrysler. The testimony was immensely helpful to the company. By accepting the mayor's help, Chrysler enters into a tacit bargain not to close down, any time soon, those ancient, obsolete and costly plants that it still operates in the heart of the mayor's city.

Meanwhile, several senators -- including the majority leader, Robert C. Byrd, and the chairman of the Finance Committee, Russell Long -- have suggested that perhaps Chrysler might become a grand experiment in employee stock options. Making the worker an owner of the corporation, they argue, will encourage higher productivity.

Speaking of productivity, the national figures for the third quarter of the year appeared Monday and show only the most minuscule improvement. The present level of productivity is lower than a year ago, a trend implying higher inflation and lower living standards. The French and German experience demonstrates that government-guided enterprise, with unions in the boardroom, can be highly competitive. Western Europe's productivity gains over this decade have been twice as high as gains in the United States. But to make that structure work, governments and unions have to be ruthless in forcing companies to consolidate, get out of profitable businesses and adapt to changing markets. That's the part of the European lesson that the Treasury, the UAW and Chrysler are going to find difficult to apply.