It airs at 11:30 PM on CBS. Set your DVR.
Chris Dunn pointed me to a nice article about the occasion here on the New York Times, but here are some excerpts.
She is still open to singing the song anywhere, "But she has vowed not to sing it for any other TV talk-show hosts after David Letterman, the man who gave her an on-air platform to perform it for nearly 30 years.
“People say, ‘He can’t demand that,'” Ms. Love explained, sweeping back her curly platinum hair. “I say, ‘He’s not demanding.’ I made a point myself, and I want to do it just for David.”
"...As [music director Paul] Shaffer said in a telephone interview about his longtime boss: “One thing about Mr. Letterman — he hates Christmas and holiday novelty songs. I could never play ‘Monster Mash’ on Halloween. No, don’t even go near it.”
"But, Mr. Shaffer said, Mr. Letterman made an exception for Ms. Love “because of Darlene’s soul.”
"Ms. Love’s thunderous and heartfelt performance went so well that she was invited back the next year, and year after year, with more and more musicians joining the occasion.
“We started expanding, with the strings and horns and everything else that we need,” Mr. Shaffer said. “And now, it’s really become a party.”