David Letterman has been hosting "The Late Show" on CBS since 1993, and for just about that long, he's been trying to convince daytime talk-show queen Oprah Winfrey to make an appearance on his show.

Letterman will finally see his wish realized on Thursday, Dec. 1, when Winfrey makes her first "Late Show" appearance. Her couch time with Letterman coincides with the opening of a Broadway musical based on "The Color Purple" that Winfrey is producing.

"What a big night that is going to be -- not only for us, not only for Oprah, but for Broadway," Letterman said Monday (Nov. 21) during the taping of "The Late Show." "You have the big 'Color Purple' Broadway opening, and then right across the street here in this theater, you have Oprah appearing here. I mean, that's what Broadway is all about -- it's a street of dreams.

"This just gives you an idea of what a big, big star this really is. She's huge. Put bygones behind us, the water under the bridge, over the dam, wherever water goes -- standing in your basement -- she's going to be here on this show and it's going to be fantastic."

Winfrey appeared twice on Letterman's NBC show, "Late Night," in the 1980s. But she has said she felt uncomfortable both times, and that's why she's resisted numerous, often public pleadings by Letterman to return to his show.

Letterman, of course, has played the rejection to the hilt, keeping an "Oprah Log" a couple of years ago that counted the days that passed without a call from her. Then there was the infamous "Oprah, Uma" bit during his hosting of the Oscars in 1995. And the fact that "Oprah" once headed a Top Ten list of "Words That Sound Cooler When Spoken by James Earl Jones."