THE whole thing was Bill Paley's idea. ''That's right, it was my idea,'' said William S. Paley. In 1981, when Cary Grant received one of the Kennedy Center Honors for lifetime achievement in Washington with, among others, Helen Hayes, Mr. Paley, the former chairman of CBS and a good friend of Mr. Grant, huddled with the former movie idol, comedian and actor and suggested that perhaps he wouldn't mind coming up to New York sometime for a similar sort of tribute, this one to be held at the Museum of Modern Art.

Well, that's exactly what happened yesterday evening at MOMA when a select group of 200 people were invited to attend a cocktail party, a viewing of excerpts from some of Mr. Grant's films and a dinner in tribute to Mr. Grant and his career in film.

Because Mr. Grant detests hoopla of any kind, does not like the word ''tribute'' and has discarded the word ''nostalgia'' from his vocabulary, the affair was handled with the utmost reticence. No formal invitations were mailed. The evening was given no special name. Instead, MOMA sent out letters, signed by Mr. Paley, the museum's board chairman, that simply said that Mr. Grant would be the honored guest at a special evening that would also benefit the annual fund of the museum.

Almost everyone responded.

''We're thrilled about the event,'' said Richard E. Oldenburg, director of the museum, ''and needless to say, we're thrilled that the benefit has added $200,000 to our fund.''

Among the guests invited to the black-tie event were Blanchette Rockefeller, one of the benefit's co- chairmen, along with Lily Auchincloss and Celeste Bartos; Victoria and S. I Newhouse Jr.; Sharon and James Hoge; Ricky and Ralph Lauren; Irene Mayer Selznick; Lally Weymouth; Liz and George Stevens; Anne and Sid Richardson Bass; Pat and Thornton Bradshaw; Helen Gurley Brown; Susan and Carter Burden; Jan and Gardner Cowles; Kimberley and Jonathan Farkas; Betty and Thomas Mellon; Peter Glenville; Carolina and Reinaldo Herrera; Carroll and Milton Petrie; Jeanne Vanderbilt, and Betsy Whitney. In other words, just the usual group of Cary Grant fans.

The evening began with cocktails at 7 P.M. in the museum's sculpture garden. Late in the day Mr. Grant was still backstage in the museum's Roy and Niuta Titus Theater 2, making last-minute preparations for the showing of film clips from his career. The show was to include excerpts from ''Notorious,'' ''His Girl Friday'' and ''Charade,'' and the 1970 broadcast of the Academy Awards presentation at which Mr. Grant, who has never won an Oscar for any role, was presented a special belated award by Frank Sinatra for his ''sheer brilliance,'' as Mr. Sinatra said. The showing was scheduled at 8 P.M. and Mr. Grant was to field questions about his career from the audience.

''It's always difficult to answer questions about my career,'' Mr. Grant said yesterday, ''but it will be especially hard with such an erudite audience.''

He winked, and went on: ''There are always a few opening ploys people use whenever they ask me questions. The first is: Why didn't I receive an Oscar for any of my roles? Well, no one voted for me, of course. But I don't carry any grudges. The second is: What is my favorite movie? Well, I don't have one. People tend to look at older antiques, including movies, with a special reverence. But I don't think antiques are any better because they're antiques.''

''The third ploy,'' Mr. Grant continued, ''is: Who was my favorite leading lady? Well, I don't have one of those either. Of course, I made more movies with some leading actresses than with others. Like Kate Hepburn, for instance. Now, Kate's a great girl.''

For her part, Barbara Grant said that there is no one movie from her husband's career that is her favorite. ''You know, I haven't seen them all,'' she said. ''But I do like 'North by Northwest' a lot. We're still trying to get copies of all of Cary's films. I have them on cassettes in our home in Beverly Hills.''

''I'll never make another movie,'' Mr. Grant said, ''but what's interesting is that almost no one ever asks why I stopped making movies. One of the reasons was that I wanted to spend more time with my daughter when she was growing up. My wife (Dyan Cannon) and I had gotten a divorce by then, which was very good copy, and every time I went to visit my daughter I was hounded by reporters at the airport. Then, a very large company offered me a job and said they would give me a private plane whenever I wanted to fly to my daughter. That made matters easier, of course.''
Then he paused and winked again. ''Of course, it was only one of the reasons.''

The rest is history. Mr. Grant worked as an executive with Faberge, is currently on the board of several large corporations, including Faberge, and in 1981, he and Barbara Harris, then 30, announced their marriage. He is 80 years old, and he does not, he says, exercise.