HIGHLAND PARK, Mich. (AP) _ Chrysler Corp. is seeking federal government permission to sell and lease back its unfinished, $1 billion technical center, a move that would give the automaker a needed cash infusion.

Chrysler Chairman Lee Iacocca has estimated the nation's No. 3 automaker invested about $1 billion in the research and engineering center north of Detroit in Auburn Hills. Company officials maintain the Chrysler Technology Center is crucial to the automaker's future.

But some critics contend that Chrysler, which lost $664 million in the fourth quarter of 1989, can't afford the facility. The fourth-quarter loss, which included $577 million in write-offs for auto plants Chrysler is closing, was the company's first quarterly deficit since 1982.

Chrysler in September sold half its 21.8-percent stake in Japanese automaker Mitsubishi Motors Corp. for an after-tax profit of $310 million. In November, Chrysler said it was considering a sale and lease back on the technical center to raise cash needed for other operations.

Earlier this month, the company sold its Gulfstream Aerospace subsidiary for $825 million.

According to the request filed Monday with the Securities and Exchange Commission, Auburn Hills Trust, organized with the assistance of Manufacturers Hanover Bank, proposes a public offering of about $800 million in securities - money that would be used to pay for Chrysler's interest in the technical center.

Auburn Hills Trust then would assign the lease to a third company, Auburn Hills Trust Services, which in turn would rent the property back to Chrysler and provide maintenance and other services under a long-term contract.

''I know the papers were filed today, that's about all I know,'' company spokesman Steve Harris said from his home Monday night. Other Chrysler officials couldn't immediately be reached for comment.

Chrysler employees are scheduled to start moving next month into a training unit on the 500-acre site, with technical and design staff slated to move to the 2.5 million-square-foot center in 1991 and 1992.

Eventually, about 5,000 people will work at the center in the 1,100-acre Oakland Technology Park, a facility for high-tech research, development and engineering.