Late-night talk show host David Letterman is a notoriously private person, but in a new interview with Oprah, he is revealing all about his marriage, an explosive cheating scandal and what he really thinks of longtime rival Jay Leno.

In a preview clip for "Oprah's Next Chapter," Letterman opens up about "Tonight Show" host Leno, who he has been in a feud with for years.

Starting off with a compliment, the "Late Show" host says Leno is "unusual," but still "the funniest guy I've ever known." He continues, saying: "Therefore, the fact that he is maybe the most insecure person I have ever known, I could never reconcile that."

Oprah also broaches the subject of Letterman's marriage to his longtime love Regina Lasko, which was rocked by a sex scandal in 2009.

The talk show host publicly admitted to sleeping with female staffers on the show after an attempted extortion plot, and apologized to both his wife and family on air. "I hurt a lot of people," Letterman explains in the interview. 

The entire interview will air Sunday on Oprah's flagship network, OWN.