But not this one! It's Broken Bells, featuring archival footage of Ringo Starr keeping the beat on a vintage-looking monitor, and with elements of other Beatles songs woven in, doing And I Love Her:
The performance above was on Letterman. The original And I Love Her was part of the A Hard Day's Night movie and album, released in 1964, and reached No. 12 on the Billboard singles chart.
Here is the lovely original version of the song: