Chip Carter, 28, second of President Carter's three sons, and his wife, Caron, 27, announced yesterday they are separating.

The brief statement released by the White House press office ended recurrent speculation that the couple's 5-year-old marriage was in difficulty. The statement said that Caron Carter and the couple's 20-month-old son, James Earl Carter IV, will move to Georgia while Chip remains at the White House. He will continue to work for the Democratic National Committee.

No explanation for the breakup was given.

"They know that their friends resepect their decision to make no further public comment," the statement said.

The separation is the couple's second in little more than a year. The first was in August 1977, when Chip returned to Georgia, leaving Caron and James Earl IV behind at the White House. Chip took over management of the family's peanut warehouse in Plains when his uncle, Billy Carter, the president's brother, resigned as managing partner. Within days, Caron and the baby joined Chip in Plains. The family stayed until January of this year when the three returned to Washington.

In a recent interview, Chip said the family business had been in need of a manager last year, and that that was a genuine consideration in his decision to return to Plains. He said he felt the media had all but ignored that and concentrated instead on his marital situation. He went home to Plains, he said, because "I could feel something changing inside. It was scary. I went back to Plains because those people have a way of straightening you out."

In the same recent interview, Carter said, "We were - we are - trying to work things out.And you keep reading about yourself every morning."

Friends of the couple said that while there have long been problems in the marriage, press reports have not helped and to some extent have made finding a solution more difficult.

Chip and Carson met in 1970, during the Georgia gubernatorial campaign. She is the daughter of Mr. and Mrs. Ben Griffin of Hawkinsville, Ga. They were married June 23, 1973. Their son was born a little more than a month after his grandfather became president.

The couple moved to the White House, settling in an apartment on the third floor, after the Inauguration. The president's third son Jeff, and his wife, Annette, as well as Amy Carter, the president's 12-year-old daughter, also live in the White House. "We couldn't afford to live anywhere else in Washington," Caron Carter told Lynda Johnson Robb in a story published last year in the Ladies' Home Journal.

The president's oldest son, Jack, a lawyer, lives with his wife in Calhoun, Ga.