President Carter won the endorsement yesterday of a key party official in Chicago, but saw the chairman of his 1976 campaign in Rhode Island defect to Sen. Edward M. Kennedy (D-Mass.).

Cook County Assessor Thomas Hynes, who had been courted by both Carter and Kennedy after leading an effort to delay an endorsement of Kennedy by the Chicago Democrats last week, announced yesterday he would support the president. At the same time, former Rhode Island governor Frank Licht said he would support Kennedy.

Hynes' endorsement was further evidence of the turmoil among Chicago Democrats over the presidential race, while Licht's move underscored the president's poor standing in Rhode Island.

Meanwhile, Robert Strauss, newly designated chairman of the Carter-Mondale campaign, issued a press release attacking Kennedy for having made five "inaccurate" statements on domestic policy issues -- including a comment on farm prices that the senator made Monday in Iowa.

"Sen. Kennedy's staff gave him the following inaccurate information, which he represented as factual to the American people," Strauss said. He went on to say that in Davenport, Iowa, Kennedy said that "the prices farmers receive have not increased at all' during the Carter administration. In fact, Strauss said, net farm income is up 35 percent since Carter took office, and corn prices in Iowa have increased an average of 32 cents a bushel over last year's prices.