Labor Secretary Ray Marshall said yesterday that Chicago has agreed to repay about $1 million in federal jobs funds it illegally used to hire ineligible and politically favored public service workers.

Using Chicago as an example of what other municipal scofflaws face in a new departmental crackdown on jobs funds abuse, Marshall said the city has also agreed to give up some its control over selection of job recipients.

"We cannot tolerate serious violations . . .," said Marshall in disclosing the action against Chicago, where political patronage was a way of life under the late Mayor Richard J. Daley and apparently lives on under his successor, Michael Bilandic.

Labor Department officials said it was the strongest action ever taken by the department in monitoring the nation's multibillion-dollar jobs program - an effort that Marshall described as "erratic" and often marked by "laxness" in the past.

Marshall said he has set up a "special review staff" under Deputy Labor Solicitor Robert Lagather to investigate other possible violations of all Labor Department laws and regulations, including but not restricted to jobs programs.

He said investigations are already planned or underway into allegations of improper use of jobs funds in New York City, Atlanta and Gary, Ind.

But he said he does not believe that violations are sufficiently widespread to merit total federal takeover of the programs, which are now administered largely by local governmennts. "I don't think the abuses are very widespread," said Marshall, "but we intend to find out."

Records from the Chicago investigation are being sent to the Justice Department for review, but Marshall said he does not anticipate any criminal prosecutions.

According to Marshall and other department sources, Chicago is receiving -129.- million to create 15,000 public service jobs under the recently expanded Comprehensive Employment and Training Act - of which it spent $965,460 to hire 438 workers under procedures that violate CETA regulations.

About 75 were given preference over other applicants because they had "political referral letters," which Marshall described as a "clear violation" of CETA rules against political favoritism in dispensing jobs.

The rest involved filling federal job slots with people already employed by the Chicago Park District or with people who would normally be hired on aseasonal basis with city funds to fill potholes.

The CETA program, which was vastly expanded by the Carter administration as part of its economic stimulus effort this year, attempts to provide public service jobs for those who cannot find work elsewhere. Jobs cannot go to existing municipal employees or persons who have been unemployed for fewer than 15 weeks.

A department official said the Chicago jobs, paying roughly $7,000 to $9,000 a year, were generally in the category of street repair, social service aid and park maintenance.

Under an agreement with Bilandic, the $965,460 that Chicago will give back to the Labor Department will be used to give jobs to those who should have gotten them in the first place, with the city picking up the tab for the improperly hired workers. Also, the Illinois Bureau of Employment Security will take over from the city the responsibility for referring job applicants, and fulltime federal compliance, Marshall said.

Yesterday's announcement resulted from an intensive three-month department probe, apparently triggered by complaints from disappointed job-seekers. Officials said there has been only one other instance of a city being forced to repay federal job funds, involving aboot $200,000 from Philadelphia.