Chip Carter is back at work at the Democratic National Committee. The 35-year-old son of the former president started work Monday as special assistant to DNC chairman Paul G. Kirk working on fund raising with Kirk's new National Finance Board of Directors and on political outreach. Carter worked for the DNC from 1977 through 1979 and was deputy southern coordinator with the Mondale presidential campaign last year . . .

Ohio Rep. John Seiberling, 67, said yesterday he underwent a successful operation for removal of a cancerous prostate gland. The surgery was performed at Johns Hopkins Hospital on April 5 . . .

Sydney J. Freedberg, the chief curator at the National Gallery of Art and one of the world's leading authorities on High Renaissance painting, will be honored for outstanding lifetime achievement in art history by the Art Dealers Association of America next month at a dinner at the Guggenheim Museum. The prestigious annual award includes a $10,000 grant and a sculpture created by the late Alexander Calder . . .

First Lady Nancy Reagan strayed from her prepared text on receiving the National Honor Award from the National Fitness Foundation in New York City Monday evening when she pointed out that she wouldn't have had a husband today if he hadn't been so physically fit when he was shot four years ago . . .

They're so serious about their ivy at Cornell University that they carry it with them wherever they go. At least that's what Cornell president Frank H.T. Rhodes is doing this weekend, when he will transplant ivy from the Ithaca, N.Y., campus to the grounds of the new Cornell Center in Washington at 2148 O St. NW for the opening of the center here Saturday . . .