The Arab gentleman dressed meticulously in pinstripes sat in the crowded booth of the coffee shop here devouring the huge double hamburger and French fries with a delight others in his position reserve for haute cuisine.

American hamburgers, said his solicitous daughter across the table, are a favorite of Suliman Saleh Olayan.

The Saudi Arabian businessman also favors American equities. Indeed, 62-year-old Olayan generally is believed to be the biggest private Saudi investor in U.S. business with hefty holdings in energy companies, railroads, utilities and banks, among others.

Although Olayan shys from discussing financial specifics, it is a measure of his portfolio that about a year ago he hired a former U.S. Treasury, William E. Simon, to manage it. Says Olayan of his reasons for hiring Simon: "As Treasury secretary, Mr. Simon was familiar with Saudi Arabia because of the tremendous financial movement we have there. And I saw Mr. Simon as a loyal and dedicated son of Wall Street, so he was no stranger to this environment."

Simon's title is deputy chairman of the Olayan Investments Co. Establishment, a Liechtenstein-registered parent company that oversees the Olayan family interests and has annual revenues of about $500 million. Chief among Simon's responsibilities is running OICE's Crescent Diversified Ltd., a British Virgin Islands company whose impressive equity holdings include one percent of Chase Manhattan Corp., the largest single interest in the holding company next to David Rockefeller.

Competrol Establishment, another firm under the OICE umbrella, holds 7.6 percent of First Chicago Corp., the holding company for the country's ninth-biggest bank, 13 percent of Donaldson, Lufkin & Jenrette, the major New York financial house, and about one percent each in First Bank System of Minneapolis, Hawaii Bancorporation, Mellon National Corp., Southeast Banking Corp. of Miami, Valley National Bank of Arizona and Western Bancorporation of Los Angeles. The Olayan interests have undisclosed investments in American real estate.

Olayan's 50 percent partner in Competrol is Prince Khaled bin Abdullah bin Abdulrahman Al Saud, a member of the Saudi Arabian royal family.

OICE with its tiny staff operates from spartan but tastefully decorated quarters on Park Avenue in midtown. Its other centers of operations are London and Athens, where it moved from wartorn Lebanon in 1976.

Appropriately, OICE's office here is housed in a building constructed in the 1940s by the old Arabiam American Oil Co. (Aramco), which has since moved from New York to what it considers the more philosophically agreeable atmosphere of Houston. Olayan credits the benevolence of Aramco with giving him a start.

The son of a spice merchant, Olayan was born in the town of Onaizah, 250 miles northeast of the capital city of Riyadh. Educated in Bahrain, Olayan returned to Saudi Arabia in 1937 and went to work as a truck dispatcher for the Aramco fleet of vehicles. Judging by his cirriculum vitae, the Americans apparently spotted Olayan as a native comer, for he was given increasing responsibilities, including the job of liaison with the Saudi government.

Tom Barger, the former chairman of Aramco, now retired and living in Southern California, said during a phone interview that he met Olayan in about 1945, and Barger recalls with a laugh that Olayan was making about $3 or $4 a day.

Barger says that Aramco had a policy of letting the more promising Arab employes take a year off to try to set up a business of their own. "We wanted to build up the local economy, realizing it would be good for us and good for the Arabs. So our policy was to give a man one year off to try to make it as an entrepreneur. If he wanted to come back, he could have his old job."

Olayan's sabbatical year came in 1947 -- and he never went back to work for Aramco. But the relationships established through Aramco served him well.

He took a loan on his house and used the $8,000 to establish a small trucking firm, General Contracting Co. It got a big contract to help in the construction of the Trans-Arabian Pipe Line. Next, Olayan founded General Trading Co., which today is Saudi Arabia's leading marketer of brand foods and cosmetic products. He also established Arab Commercial Enterprises, now the largest insurance brokerage and re-insurance group in the Middle East.

A short, strapping man who puffs long cigarettes as he chain-sips cups of coffee, Olayan has an engaging personality and an informality that American businessmen probably find disarming, but in contrast with some of the more flamboyant Arab wheeler-dealers, Olayan is decidedly conservative. For example, in an interview in the current issue of a magazine called Leaders, Olayan was asked, "What annoys you most?"

He replied: "What annoys me most are things that I consider to be in poor taste: lack of politeness in people; cars driving around the street blowing horns; lack of attention to our elderly; and lack of affection for our children."

Olayan spends most of his time in Riyadh, but he also maintains residences in London and New York. His third wife, Mary, is an American who worked in Aramco's Washington office. He has three daughters, two of them in banking, and a son, Khaled, who is chairman of the Olayan Saudi Holding Co., the chief operating group in Saudi Arabia.

In 1976, a 40 percent interest in this company was acquired by a Hong Kong-based investment group of Jardine Matheson & Co. Ltd. Another investor, American Express Co. has a much smaller interest in Saudi Holding Co.

That company is involved in a staggering array of businesses, including plastics, agriculture and explosives, and joint ventures with Bechtel for engineering services, McAllister Brothers of New York for tugboat services, interior architectural and design services with Staats Co. of Boston, banking with Barclays, chemicals with Nitro Nobel AB of Sweden, to list a few.

The Saudi businessman generally demurs from discussing specifics of his U.S. interests, and since most of his investments purposely are kept below the 5 percent level at which federal law makes disclosure mandatory, there is no public record of his exact holdings. But he will provide percentages. He says that 18.8 percent of his U.S. portfolio is invested in oil and gas securities, 15.4 percent in utilities, 11.5 percent in banking, 5.3 percent in rails, 4 percent in office equipment, 2.6 percent in electronics, with the balance in various industries.

Olayan has refused steadfastly to join the boards of companies in which he invested, but recently he made an exception for Mobil Corp. Olayan has long served as a consultant to Mobil in Saudi Arabia, where the company has a massive and diversified interest. Nevertheless, the invitation to join Mobil's board put him in a quandary, considering his policy.

"I consulted friends and associates, and they said: 'You must accept it.' It was a flattering invitation," he says, and apparently one he could not refuse.

The Olayan portfolio includes what he describes as an "insignificant amount" of stock in Washington Gas Light Co., which he describes as a "traditional company." He notes that the stock recently rose when the company hit a large gas well, then went down. "We looked at it very carefully," Olayan says. "We thought it was a good company without the well, and with the well it's a very fine company."

In the 1960s, Citibank, then First National City Bank, made the mistake of calling a loan because it concluded that Olayan was overextended. "It was a misunderstanding," Olayan says, then adds: "We didn't do business with them for a while . . . until about six or seven years ago."

Olayan thinks that reports of the amount of Saudi oil money invested in this country have been exaggerated in the press. "People forget that the surplus belongs to the government, and the government doesn't invest for profit in our country, let alone elsewhere. We have no sidewalks, telephones. We are building from scratch. So these funds are just temporary surpluses."

With his big investment in publicly owned First Chicago, Olayan says he has become a public person for the first time.

Increasingly, he receives interview requests, is asked to give speeches and write pieces on such subjects as the need for a Palestinian state and on OPEC, the Organization of Petroleum Exporting Exporting Countries.

Moreover, his outside investors, such as Jardine Matheson, have brought about a change in the way Olayan does business. For example, the complex organizational chart of his companies that once was filed only in his impressive memory is now detailed in a slich brochure. And on the cover his name, Olayan, has become part of a jazzy logo.

It's not clear, however, whether he's happy with his new celebrity because for even with his new high profile, Olayan remains a very private person.