"I THINK of Kukla and Ollie the way Itzhak Perlman would think of his Stradivarius," says veteran puppeteer Burr Tillstrom. "Maybe that's putting myself in too high a rank. But they are very sensitive instruments, too, and they are important to me." Tillstrom, 65, created the Kuklapolitan cosmos and carved a special niche in television history in the process.

With "Kukla, Fran & Ollie," Tillstrom and his manual menagerie, which included such classic and classy characters as Kukla the bulb-nosed clown, the one-toothed, flameless Oliver J. Dragon (Ollie), snooty ex-opera star Madame Ophelia Ooglepuss, mailman Fletcher Rabbit, jet-propelled Buelah Witch, and the very human Fran Allison, were the first program on the new NBC national television network, which ran, live and unscripted, five days a week for 10 years.

"I think I'm very un-self-conscious about what I do," Tillstrom says, explaining his apparently endless energy. "I really try and entertain myself, and Fran, too. I believe in activity and youth. You won't believe this and I hate to say it, but Fran is 10 years older than I am. And she's still like a kid! It's very easy to break her up with the characters. We work together as often as we can.

"When I was getting started on television, there were just 3,000 sets in Chicago," Tillstrom recalls. "Within a year and a half there was a national network growing NBC . In those days the networks grew by cities. Finally, it was like the Golden Spike, when they hooked up from coast to coast. I was very aware of it all--it was one of the most exciting things in my life.

"I toured with RCA in 1939-40, demonstrating television, and we wound up at the World's Fair in New York City. We did a little live closed-circuit show, which they showed in 10 little living rooms. People were ushered in, about six to eight per room, and they would sit down and watch TV. One of the watchwords then was 'Television is intimate.' I think it's lost sight of that now."

Tillstrom says he was influenced by his parents, both of whom he says had theatrical talent, and by movies and radio. "I was just old enough to catch the end of silent movies, Buster Keaton and Charlie Chaplin. And radio, too, especially "Vic and Sade" and Jack Benny.

"As a child, I always tried to mimic performances and movies I saw with small figures, stuffed teddy bears, dolls, anything I could make move. There was very little written about puppets, but sometimes a touring company would come through. I found a book and made some marionettes."

After high school, Tillstrom was offered a job with the WPA Federal Theater's Marionette Project. "I gave up the University of Chicago to do the job. I hate to say it, but I was always glad I did it," he says. Tillstrom produced a puppet version of Gertrude Stein's " 'Identity' or 'I Am I Because My Little Dog Knows Me.' " "Thornton Wilder was teaching at the University of Chicago and he came out and coached us. I remember he said, 'Don't worry about what it means, just listen to how beautiful the words sound.' "

Kukla, Tillstrom's first puppet, who will be 50 years old in 1986, was named by the Russian ballerina Tamara Toumanova in 1936. "I was a great ballet buff, still am, and I took Kukla backstage. She was sitting there putting on makeup, looking in the mirror, and I brought him up over her shoulder. He appeared behind her and patted her cheek and hugged her, and she looked up with joy and surprise and said in Russian, "Oh, Kukla!" which means 'doll.' "

"I made Kukla as a gift for a friend who taught me how to make hand puppets. But I loved him so much, I kept him for myself."

Tillstrom speaks about his creations as separate entities, chuckling over Ollie's mischievous attempts to crack up the young host of the "AM Chicago" television show last week. "A playwright will talk about his characters as living people, so will an actor. Once you've established a character, they do have their own special life."

Tillstrom says he has gone through many versions of his original puppets, but he saves them all, and refuses to exhibit them. "I never show my puppets--I find it hard to have them exposed lifeless."

Besides working on a children's book, "a Thurberesque fairy tale" starring Kukla and Ollie, Tillstrom is now performing "Kukla & Ollie Live!" at the 130-seat Goodman Theatre Studio in Chicago, still operating all the puppets and doing all the voices for the show, which includes 14 songs, a musical director/pianist and a sentimental video tribute to Fran, who chose to stay at home in California this time.

"We're performing Christmas Eve, our closing night," Tillstrom says. Will he bring the puppets out to entertain Christmas visitors? "Oh, no," Tillstrom says. "I have my life, they have theirs."