Chip Carter and his wife, Caron, attended church services yesterday with the President and Mrs. Carter, amid reports that the young couple are having marital problems.

They sat side-by-side, whispering and holding hands during the service.

Rosalynn Carter's press secretary, Mary Hoyt, said she did not know what their appearance together in church signified. The White House is already on record denying the rumors of a separation.

Despite their Sunday morning appearance together, Hoyt said there was no change in Carter's plans to leave Washington and return to Plains, Ga. His wife and 6-month-old son, James, will remain in the White House with the President and First Lady.

The Associated Press reported yesterday that the White House has also declined to say whether Chip is still living in the White House.

Hoyt said Carter plans to leave for Plains early this week to "help out" with the family peanut business.

Earlier this month, Chip resigned his $8,000-a-year part-time job with the Democratic National Committee. Saturday, his uncle Billy Carter announced plans to give up management of the family business in Plains on Sept. 1, saying he wanted to devote more time to his family.

Yesterday, Hoyt said that Chip's departure was "just a family decision," and that Caron and their son would join Chip "at a later date."

Meanwhile Caron Carter and her son will accompany the First Family to Camp David for a brief vacation Tuesday.