The long-awaited and much-hyped interview of David Letterman by Oprah Winfrey on Winfrey’s "Oprah’s Next Chapter" aired Sunday night, Jan. 6, 2013.

Here’s an edited transcript. We begin with Letterman explaining his rivalry with Jay Leno.

Oprah Winfrey: There is an assumption that since you didn’t get [to be the host of the "Tonight" show when Johnny Carson retired] and Jay Leno did, that that’s where the rivalry between the two of you started. Is that true?

David Letterman: No. No. The rivalry — Jay and I were friends. We were always friends before all of this happened. He has a way — he’s an unusual fellow. I’ve never met anyone quite like Jay. And I will say — and I’m happy to say — that I think he is the funniest guy I’ve ever known. Just flat out, if you go to see him do his nightclub act, just the funniest, the smartest, a wonderful observationist and very appealing as a comic. Therefore, the fact that he is also maybe the most insecure person I have ever known … I could never reconcile that. You’re the best. Why are you doing things to support this insecurity. Why …

Winfrey: Everyone says you’re insecure too.

Letterman: Not to the degree this man is. This is the guy that is documented as hiding in a closet as they are having a business meeting at NBC to decide who would get the "Tonight" show chair. I have not hidden in closets — not for that purpose. I’ve found myself, sadly, in closets …

Winfrey: But not for that purpose.

Letterman: But not for that purpose.

Winfrey (incredulous): So the reason for your rivalry is because of his, Jay’s, insecurity?

Letterman: Well, how it manifests itself. And that’s all I want to say about that, because — I’ll just tell you this. When we were all kids — and I do think Jay and I are still friends …

Winfrey: Would he think so? 

Letterman: I think so. I think so. Because I’ve got too much on him (laughs). You know. When he and I were kids, and somebody would go on like the "Merv Griffin Show," and if he didn’t do well, Jay would come (does his Jay "whine"), "Did you see Larry on the ‘Merv Griffin Show’?" "No, I didn’t." "Yeah, I got a tape back at the house. Come on and take a look at it." And he’d invite you back to watch one of our fellow comics bomb. And I was like, "Oh, Jay, stop that. That’s silly."

Winfrey: When we did the Super Bowl spot two or three years ago, you all hadn’t communicated in years and years and years. Was that awkward for you?

Letterman: No, it was great. Because, as he and I discussed then, our way of life at the Comedy Store is exactly the way you would think it would be for a group of comics. It was tinged with sarcasm and ugliness and insult, but everybody loved it. We thrived on it. We could call each other names, we could steal each other’s jokes, we could make fun of each other’s girlfriends, and this and that and this and that. You take that out of the Comedy Store and all of a sudden it’s "oh my god, it’s Civil War, we can’t believe it." But the truth of it is that the way Jay and I have behaved toward one another is the way comics tend to behave toward one another.

Later in the interview Oprah, for the first time in close to 25 years, tells her version of the beginning of the feud between her and Letterman:

Winfrey: I want to know if this is true or not. Did you actually think I was actually angry with you or did it make a better joke?

Letterman: As far as I know, the genesis of this …

Winfrey: People think we still have a feud going. Do you want them to think that?

Letterman: No. I did for a while. Because it was great for me. When I would bait you about coming on the show, oh, big laughs.

Winfrey: For 82 days straight you did.

Letterman: Yeah.

Winfrey: How did this start?

Letterman: I think it was one time we were coming to do the show in Chicago, and I called you. I’ll never forget this.

Winfrey: Yes.

Letterman: And I got you on the phone. And you barked at me and you said, well, the least you could’ve done was call me on a hard line.

Winfrey: I barked at you? I barked at you?

Letterman: Yeah. I said, "Oh, no, I didn’t even get beyond hello and I pissed her off." So then I said, "Oprah, we’re doing a show in Chicago, and we’d love you to be on it." [And you said] "I am totally out of town. I am totally out of town." So in my mind that’s what it was.

Winfrey: Let me tell you what my memory is. Would you like to hear mine?

Letterman: Yes.   

To read the rest of the Letterman-Oprah interview, please click here.