Chrysler Corp. and Mitsubishi Motors Corp. last night signed a $500 million agreement to build 180,000 subcompact cars a year in the United States, beginning in 1989, according to industry sources. The $500 million initial investment -- one of the largest to be made by a Japanese auto manufacturer -- will be split equally between Chrysler and Mitsubishi, the sources said.

The plant is to be built in the Bloomington-Normal, Ill., area, according to The Associated Press. That decision is to be announced at a new conference today in Detroit.

To attract the plant, the AP reported, the state of Illinois and Bloomington-Normal offer the automakers about $10 million worth of land, $20 million in local real estate tax breaks over 10 years and various other incentives valued conservatively at more than $100 million.

The joint venture between Chrysler and Mitsubishi is expected to yield 2,500 production jobs and 9,000 jobs in related industries when the plant is operating on two shifts, the sources said.

Details on the pact are to be announced today in Detroit at a news conference with Chrysler Chairman Lee A. Iaccoca and Toyoo Tate, president of Mitsubishi Motors.

The agreement means that Mitsubishi will become the fifth Japanese automaker to assemble or to have announced plans to assemble cars on U.S. soil. It also means that the Japanese car companies think that the U.S. Congress, in an effort to change the balances of trade between the United States and Japan, is on the verge of enacting protectionist legislation that could severely restrict the flow of automobiles and other Japanese products into the United States.

Building their cars in America, either on their own or through a joint venture, is one way to get around barriers that could hurt the Japanese companies' growing share of the U.S. auto market.

Japanese cars account for 25 percent of automobiles sold in the United States.

Toyota Motor Corp., Nissan Motor Co,. Ltd. and Honda Motor Co. Ltd. are producing passenger vehicles in this country.

Industry analysts think that Japanese automakers will have the capacity to build nearly 1 million cars a year in the country by 1990.

Chrysler and Mitsubishi have had a 15-year relaationship in which Mitsubishi basically supplied its U.S. counterpart with high-quality subcompact cars. Chrysler imported nearly 100,000 of them from its Japanese partner in 1984.

Chysler is asking Mitsubishi to supply it with 200,000 built-up cars a year for U.S. sales. Mitsubishi also supplies Chrysler 2.6 liter 4-cylinder engines. Chrysler plans to order a larger V-6 engine as well.

The Chrysler-Mitsubishi pact comes one week before the contract deadline between Chrysler and the United Auto Workers.