The musical guest for the evening will be Chris Young.
"Late Show" airs weeknights on CBS at 11:35 PM ET; check local listings.
On the Twentieth Century, which will co-star Peter Gallagher, will begin previews Feb. 12, 2015, towards a March 12 opening night. It is scheduled to play a limited 20-week engagement through July 5 at the American Airlines Theatre.
Chenoweth won the Tony Award in 1999 for her performance in You're A Good Man, Charlie Brown. She was nominated in 2004 for her performance in Wicked and has also been seen on Broadway in Steel Pier, Epic Proportions, The Apple Tree and Promises, Promises. The actress is also known for her award-winning film and television work, including "Glee," "Pushing Daisies" and the recent ABC series "GCB."