A different song with the same name, written by Leon Russell and Bonny Bramlett, was sung by Joe Cocker.
Writing and recording
The song was written during Lennon’s Bed-In honeymoon: when asked by a reporter what he was trying to achieve by staying in bed, Lennon answered spontaneously “All we are saying is give peace a chance”; Lennon liked the phrase and set it to music for the song.. He sang the song several times during the Bed-In, and finally, on 1 June 1969, in Room 1742 at the Queen Elizabeth Hotel in Montreal, recorded it using a simple setup of four microphones and a four-track tape recorder rented from a local recording studio. The recording session was attended by dozens of journalists and various celebrities, including Timothy Leary, Rabbi Abraham Feinberg, Joseph Schwartz, Allan Rock, Rosemary Woodruff Leary, Petula Clark, Dick Gregory, Allen Ginsberg, Murray the K, Al Capp and Derek Taylor, many of whom are mentioned in the lyrics. Lennon played acoustic guitar and was joined by Tommy Smothers of the Smothers Brothers, also on acoustic guitar.
The song was credited to Lennon/McCartney (John Lennon and Paul McCartney) and published by Northern Songs (now Sony/ATV Music Publishing). On some later releases of the song, only Lennon is credited; viz. the 1990s reissue of the 1972 album Live in New York City, the 2006 documentary The U.S. vs. John Lennon (in which the song appears), and the 1997 compilation album Lennon Legend: The Very Best of John Lennon (and its DVD version six years later). Lennon later stated his regrets about being guilty enough to give McCartney credit as co-writer on my first independent single instead of giving it to Yoko, who had actually written it with me.  However, it has also been suggested that the credit was a way of thanks to McCartney for helping him record “The Ballad of John and Yoko” at short notice.
- John Lennon Inspired Songwriter Finishes Unreleased Beatles Song (prweb.com)
- The life and death of John Ono Lennon (am74wmap.wordpress.com)
- Paul McCartney in the Millennium Stadium â The Review, Arts and Literature (visitwales.co.uk)