"Rainbow Connection " is a cover of the Kermit the Frog song performed in the "The Muppet Movie". The song has come to epitomize the ideals and artistic spirit of Muppet creator Jim Henson.
Jonathan Coulton performed a cover of "Rainbow Connection" during John Hodgman's Little Gray Book Lecture #2, "Hints on Public Singing". To date, this is the only known time Jonathan has played it.
"Rainbow Connection" has not as of yet been officially recorded; however, a copy of the Little Gray Book Lecture performance is available at awryone's download page, a collection of older Jonathan Coulton recordings.