The United Auto Workers and the Chrysler Corp. opened contract negotiations yesterday with company profits up and the union hoping to regain at least some of the concessions it made 18 months ago when the company won its famous "bailout" contract.

"The timing is great," UAW president Douglas Fraser said as the bargainers gathered at Chrysler headquarters in Detroit. He was referring to the company's $106.9 million profit of the past three months, announced Monday.

"Now it's time for Chrysler workers to begin that long, long road back to wage equity and parity with the General Motors and Ford workers," he said.

Fraser, who was given a seat on the company's board as part of the last contract agreement, has vowed "no more concessions" to Chrysler. The union has listed as priorities the restoration of its frozen cost-of-living payments and job security. Its contract expires Sept. 14.

Under pressure from the federal government in 1980, union workers granted the company concessions at an estimated worth of $880 million. The government then guaranteed $1.2 billion in loans to save the company.

Still on shaky ground in domestic auto sales, Chrysler reportedly considers it necessary to keep its edge over Ford and General Motors in employment costs. Chrysler's workers receive from $2 to $3 less per hour than those at the other two companies.

Both sides seem aware of Chrysler's precarious health. As one UAW spokesman in Detroit said yesterday, "The auto workers are not insane. We wouldn't save a company and then put it out of business. Of course, we realize you can't have job security if there's no company."

The number three car maker has closed 20 plants in the past three years. From a 1978 high of 165,000, its work force has been cut to 43,200.

Chrysler's second-quarter profit, its highest from car and truck sales in more than five years, was attributed primarily to cost cutting and sales of luxury cars.

Chrysler sales are down by 12.8 percent compared with 1981. Domestic car sales overall are down by 11.5 percent.