On the talk show, Once co-stars Steve Kazee and Cristin Milioti offered a performance of the Oscar-winning song "Following Slowly" backed by the Broadway company of actor-musicians.

The new musical opened March 18, following previews that began Feb. 28, at Broadway's Bernard B. Jacobs Theatre. The production transferred to Broadway from an Off-Broadway engagement at New York Theatre Workshop in 2011.

The cast of Once features Kazee (110 in the Shade, Spamalot) as Guy and Milioti (Off-Broadway's That Face, Stunning, The Heart Is a Lonely Hunter) as Girl. Also in the troupe are David Abeles, Will Connolly, Elizabeth A. Davis, David Patrick Kelly as Guy's Da, Anne L. Nathan as Girl's mother, Lucas Papaelias, Ripley Sobo, Andy Taylor, Mckayla Twiggs, Erikka Walsh, Paul Whitty and J. Michael Zygo.

Here's how the producers characterize the musical: "[Once] tells the story of an Irish musician and a Czech immigrant drawn together by their shared love of music. Over the course of one fateful week, their unexpected friendship and collaboration evolves into a powerful but complicated romance, heightened by the raw emotion of the songs they create together. Brought to the stage by an award-winning team of visionary artists and featuring an ensemble cast of gifted actor/musicians, Once is a musical celebration of life and love: thrilling in its originality, daring in its honesty... and unforgettable in every way."

To check out Once's performance on "Letterman," look below: