Last month at their Chamber Music Chicago “Outreach Series” concert for children, a young girl stood up and asked the Kronos Quartet why they don’t play Mozart. “Don’t you like him?” she asked, sincerely puzzled.

“Yes, yes, very much,” David Harrington, Kronos leader, founder, and first violinist, answered. “He’s a real nice guy!”

“Didn’t he write music for your kind of group?” she inquired.

“Yes, Mozart wrote a lot of music for quartet. But a lot of people play that style of music, so we decided to play music that we most enjoy playing, the majority of which is written right now.”

The girl still seemed troubled, so Harrington went on: “In Mozart’s time, which was over 200 years ago, people only played and heard music of their own time. And that’s what we do. So what were doing is not really a new idea, but an old idea.”

“Why do you all move around while you’re playing?” asked a young boy.

“It helps us to move in rhythm to the music,” Harrington said. “Most of the music you’re probably used to hearing has a drummer, and it’s the drummer’s job to keep the beat. Since we don’t have a drummer, it’s everyone’s job in our group to keep the beat.”

“Where did you get the idea to play Hendrix,” asked an older boy, “and have you been criticized for it?”

“A long time ago, I grew up with the music,” said Harrington. “And my wife went to the same high school as Hendrix. I really liked the music, still do, and I wanted to play it. As for criticism, we get criticized for a lot of things.”

By now, just about everyone has heard of the controversial Kronos Quartet, the string quartet that dresses and wears hairstyles more like a rock group than a classical act, the quartet that plays music no earlier than that of Bartok, the quartet that plays arrangements of music by Jimi Hendrix and Thelonious Monk.

But under the carefully constructed (and enormously successful) sassy box-office image the four enormously talented and dedicated musicians who have all made great personal sacrifices to keep the group so extraordinarily tight and polished. They have been playing together virtually every day for a decade now. The unspoken communication between them is truly rare and remarkable in any performance genre; the four have really learned to think and play as a unit.

“This year we’ve played 140 concerts all over the world, in addition to having recorded several albums,” says Harrington. “Despite that, no one in the group has ever lost their cool, and, in fact, we’re all having some really fascinating musical experiences together.”

The Kronos Quartet concerts have been popular in Chicago–each of their Chamber Music Chicago performances has sold out.

When news that the Monday night concert at the Royal-George had sold out reached CMC executive director Susan Lipman, she asked the quartet to play another concert in a very different setting.

The result, called “Jazz With the Kronos,” will feature music of Thelonious Monk, Bill Evans, Terry Riley, Arvo Part, Kevin Volans, Astor Piazzolla, and Peter Schulthorpe. The concert will take place on Father’s Day, June 19, at 6 PM at City, 361 W. Chestnut; $20. Call 242-6237 for information.