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Supermodel Kendall Jenner takes Jay Leno for a spin in her '56 Corvette

TV star and Olympian Caitlyn Jenner has been friends with Jay Leno for almost 30 years. One day, when she brought her daughter Kendall to his garage, the 20-year-old supermodel fell in love with Jay's 1957 Corvette.

She wanted one of her own. And Jay helped find her something close. Now, on an episode of CNBC's "Jay Leno's Garage," he visits the Jenners in Malibu to check in on Kendall and see how she likes driving her 1956 Corvette.

"You know," Jay says, upon seeing the stunning blue-and-white car, "that's actually the first year Corvette got real serious about building a sports car."

Since then, collectors have gotten serious about having them. This one originally sold for a little over $3,000. Now it's worth more than $80,000.

Helpfully, it's in almost perfect condition. Kendall's car was actually rebuilt by a member of the National Corvette Restorers Society. It's as close to original as possible.

Caitlyn can't say enough nice things about her daughter's car. Though she does make one major protest: "She won't let me drive it, Jay," Caitlyn says.

Caitlyn Jenner watches as her daughter Kendall goes for a classic car joy ride with Jay Leno.
CNBC (from “Jay Leno’s Garage”)
Caitlyn Jenner watches as her daughter Kendall goes for a classic car joy ride with Jay Leno.

Kendall says her car regularly draws all sort of attention, especially from guys. Often those who are more than three times her age.

And giving Jay a ride only adds fuel to that fire.

As they're about to pull out of the driveway, Caitlyn asks, "Shouldn't I be concerned? My daughter leaving with an older man?"

Jay responds, "Well, the nice thing is, they don't get much older."

Soon, they're off and down the road, with Kendall driving.

Kendall's first vehicle was actually a 2012 Range Rover. It was a gift from her parents on her 16th birthday. A premature one, it turned out: she failed her driving test for forgetting to use her blinker. Twice.

But she's a better driver now. And she needs to be. Classic cars are more high maintenance. For example, there's no power steering.

Jay Leno and Kendall Jenner cruise down the open road in her ’56 Corvette.
CNBC (from “Jay Leno’s Garage”)
Jay Leno and Kendall Jenner cruise down the open road in her ’56 Corvette.

"There's just things to it that you kinda gotta get used to," Kendall says about having to concentrate. "I also love that I can say that I can drive this car."

Jay agrees, "Not many people your age can even drive stick."

Kendall also says she's never let any of her friends behind the wheel. That is music to Jay's ears. "Excellent," he says. "True car girl. Never give it to a valet. And don't let your idiot friends drive it."

Before the ride ends, Leno asks one last important question he feels every car guy wants to know: "Are you impressed by a man's car?"

Kendall's answer is simple. "If they have a classic car. Yeah."

CNBC's "Jay Leno's Garage" airs Wednesdays at 10 p.m. ET.