Thomas D. Barrow, until recently a top executive of Exxon Corp., was elected today to be the chairman and chief executive officer of the embattled Kennecott Copper Corp., the country's largest copper producer.

Kennecott, meanwhile, announced it will go to the Supreme Court to appeal a lower court ruling ordering it to hold a rerun of last spring's proxy challenge, led by Curtiss-Wright Corp., to Kennecott's board of directors.

On Thursday, the U.S. Court of Appeals denied Kennecott's application for a stay of the earlier ruling.

Frank Milliken, 64, who is stepping aside as Kennecott chief executive after 17 years at the helm and who personally has been a key target of criticism of Curtiss-Wright's proxy challenge, will become chairman temporarily of the Kennecott board's executive committee, and then retire next January when he reaches age 65.

The appointment of Barrow, 35, did not come as a surprise since there had been numerous press reports that he had been negotiating with the Kennecott board for the company's top post. He resigned from Exxon Nov. 15 where he had been a senior vice president and was at one time considered in the running for either the presidency or chairmanship of the world's largest oil company.

A petroleum engineer and geologist by training, Barrow was responsible for exploration, production, and employe relations at Exxon as well as being the chairman of the company's investment advisory committee. He earlier had served as president of Exxon U.S.A., the corporation's principal domestic operating division, a position his father had held when the subsidiary was known as Humble Oil.

Barrow will take over Kennecott at a time when it faces continuing profitability problems because of the sustained worldwide slump in demand for copper on top of the difficulties generated by the Curtiss-Wright proxy challenge.

For the first nine months of 1978, Kennecott lost $1.25 million, an improvement over the first three-quarters of 1977 when the company lost $4.4 million. For all of last year, Kennecott earned $7.3 million on sales of $977 million.

In an interview with the Dow Jones News Service, Barrow said today he had no plans to change substantially the direction Kennecott is heading and indicated he supported the company's acquisition last year of Carborundum Corp. for $567 million in cash -- a move that angered many shareholders and triggered the proxy battle.

Curtiss-Wright Chairman T. Roland Berner, in mounting the challenge said that if he gained control of the copper company he would sell off Carborundum and distribute the proceeds to shareholders. Kennecott had bought the upstate New York abrasives manufacturer with part of the $1.2 billion it received when it sold the Peabody Coal Co. on orders from the Federal Trade Commission.

"Carborundum is a little 3M," Barrow told Dow Jones, adding "it has got a whole lot of businesses" and indicating it represented the kind of diversification the copper producer needed to smooth the swings in the copper market.

Barrow said he did not intend to lead Kennecott into the oil business, but it should continue to look for other acquisitions.

Kennecott itself has been rumored as a possible acquisition target. Standard Oil Co. of Indiana (Amoco) in September confirmed the two companies had held talks about the possibility of "some form of association." But last month, Wall Street sources said a complex plan for Amoco to buy Kennecott for close to $1 billion and to then dispose of Carborundum to the Continental Group collapsed.