Call it "Strangers on a Plane," and in leading roles cast a noted syndicated columnist, a former psychiatrist who has become one of the world's leading dealers in precious metals, and a voluble Washington bureaucrat. Add a passel of big names in cameo roles, and for locations a plane cabin, LaGuardia airport, a posh flat on Gracie Square on the upper east side and a Manhattan art gallery.

Then there's the check for $24 million.

It all began innocently enough when columnist Joseph Kraft boarded the 2 p.>m. shuttle last Tuesday, bound for LaGuardia. Kraft was excited, for that evening there was to be a party to open a showing by his artist wife, Polly, at Kornlee Gallery on West 52nd Street.

Kraft spotted Laurence H. Silberman, the former ambassador to Yugoslavia, and the two men sat together and began chatting.

It was hot and crowded, so Kraft took off his coat and placed it in an overhead compartment. Soon, a big man squeezed past Kraft and Silberman, tossing his coat up into the same overhead compartment before settling into the window seat to pore over reams of computer printouts.

At LaGuardia, Kraft pulled down Silberman's raincoat and a suitcoat he thought was his; then with the coat under his arm, he dashed for a taxi. It was not until later, when he was hurrying out to the party, that he realized the terrible truth - the coat he grabbed was not his.

In the pocked of the coat he found a well-stamped passport, belonging to a Henry Jarecki. And when Kraft saw Jarecki's picture, he realized that he had taken the coat belonging to the big man in the third seat.

But what really shook Kraft was the next item he pulled from the coat - a check made out to Jarecki in the sum of $24 million and signed by one William T. Bagley.

Kraft also found a notebook containing Jarecki's home telephone number. "Jarecki's wife answered the phone," Kraft recalled. "I identified myself, said I had his coat, and added that he probably wanted it back because it had a $24 million check in it."

Kraft was spending the night at the Gracie Square apartment of Peter G. Peterson, the former secretary of commerce who is chairman of the prestigious investment banking firm, Lehman Brothers, Kuhn, Loeb, Inc.

As it happens, Jarecki is a celebrity in his own right. Dr. Jarecki gave up teaching psychiatry at Yale University Medical School in the late 1960s to test his theories of international metals price movements.

He is now chairman of the hugely successful, low-profile Mocatta Metals Corp., one of the biggest dealers in precious metals. In its Iron Mountain Depository under 26 Broadway is perhaps the world's richest private lode of gold and silver.

Back at LaGuardia, Jarecki had chased Kraft, then turned vainly to Eastern's lost-and-found department. Driving home with Kraft's coat, he got a call on his car phone from his wife, who gave him the Peterson number.

Meanwhile, Kraft, who was eying the clock, fearful that he would be late for his wife's opening party, also was making calls. He had recently interviewed Frank Borman, chairman of Eastern Airlines, so he called his office, which later reported back that Jarecki had taken Kraft's coat.

And when he saw a World Bank stamp in Jarecki's passport, he called former defense secretary Robert McNamara, now chairman of the World Bank, on the chance that Jarecki worked for that organization. McNamara checked and assured Kraft that he did not.

Then the Peterson phone rang, and, Kraft says, a voice with perhaps a Spanish accent said: "is this the Peterson residence? Are you Joseph Kraft, the columnist? Well, this is a lawyer and I just want to tell you that you are in heavy trouble."

The identity of that caller remains unknown. But the call caused Sally Peterson to order the doorman not to permit the mysterious Jarecki upstairs.

Kraft grew more curious about the peripatetic Jarecki when he noted that his passport number began with a "D." The columnist took this letter to mean it was a so-called diplomatic passport, the kind of passport Bert Lance once used and which supposedly is distributed only to leading government figures.

The State Department said yesterday, however, that the "D" refers to the year the passport was acquired. Diplomatic passports use "X."

At 4:50 p.m., the doorman rang the Peterson apartment to say Jarecki was there for his coat. Downstairs, Jarecki and Kraft met, exchanged coats, and Kraft claimed he was missing some things from his. Jarecki said he didn't know anything about them, and he added: "By the way, the $24 million check was a joke."

Jarecki's identity was established when Kraft and Sally Peterson finally reached Polly Kraft's Show. No less a person that former ambassador George Ball, who knows Jarecki well, reassured them that they were dealing with a person of some substance.

William T. Bagley, the name on the Riggs National Bank check, is the gregarious chairman of the often embattled regulatory egency, the Commodity Futures Trading Commission. Yesterday at his office Bagley told about the check.

It seems that last January the CFTC, which oversees some of the German-born Jarecki's trading operations, adopted certain regulations that cut into his business. After the meeting, Bagley sought to console Jarecki over a cup of coffee.

"How much is this going to cost you?" he asked. "Oh, about $24 million," Jarecki tossed back. At which point Bagley wrote the check. "That should cover it," he said.

In Bagley's office is another personal check, this one framed, written to the Governor Edmond G. (Pat) Brown, dated Apr. 20, 1966, for $4.6 billion. THis one he presented to governor, Bagley says, to cover the California state budget when, as a Republican legislator, he was accused by Brown of delaying its passage.

When asked why he had this habit of writing checks, Bagley answered: "Hell, I don't make any money here, so I might as well have a little fun."