SPARKS flew the instant “Survivor” host Jeff Probst laid eyes on “Kristin” star Kristin Chenoweth — and now the two are secretly dating.

But their blossoming romance may not survive the challenge of each other’s incredibly busy schedules, pals say.

“They’re smitten with each other,” a source close to Kristin told The ENQUIRER. “It’s been hard for them to get too hot and heavy — but it’s not because they don’t want to.”

The pair met not long ago at a charity event Jeff, 39, was hosting in Las Vegas. Sexy Kristin, 32 — who’s also a talented Broadway musical songbird — was performing.

“Jeff had never even heard of her, despite her Tony award for ‘You’re a Good Man, Charlie Brown,'” said the source. “But Kristin had never watched ‘Survivor’ so she had no idea who he was either!”

Immediately blown away at the sight of Kristin, “Jeff just walked right over to her and told her, ‘You’re the most beautiful girl I’ve ever seen.’ That was it. He walked away, acting cool — but later got in touch with her agent and got her phone number!

“They talked on the phone a lot and after many scheduling problems, they managed a first date — to see ‘Pearl Harbor.’

“They really hit it off — and now talk constantly on the phone and by e-mail. When Kristin was taping Rosie O’Donnell’s show recently, Jeff called her to wish her good luck, and say that he’d be watching when the show aired.”

Probst recently filed for divorce from his wife of five years, Shelley. And Kristin recently broke off an engagement to actor Marc Kudisch, said the source.

Kristin has been consumed with working on her brandnew NBC sitcom and pre- paring for concerts at New York’s Carnegie Hall and the Hollywood Bowl. And Jeff is set to head to Africa for six weeks to shoot “Survivor 3.”

Divulged the source, “Yet, he’s now trying to delay his departure by one day so he can catch Kristin at the Hollywood Bowl on July 2 — the day he was originally set to go. For now, Kristin has no plans to travel to Africa to be with Jeff.

“But if they can ‘survive’ the time and distance they’ll be apart, there’s no telling where this relationship could go!”