Wikipedia:
Chaplin's compositions produced three popular songs. "Smile", composed originally for Modern Times (1936) and later set to lyrics by John Turner and Geoffrey Parsons, was a hit for Nat King Cole in 1954.[398] For Limelight, Chaplin composed "Terry's Theme", which was popularised by Jimmy Young as "Eternally" (1952).[400] Finally, "This Is My Song", performed by Petula Clark for A Countess from Hong Kong (1967), reached number one on the UK and other European charts.[401] Chaplin also received his only competitive Oscar for his composition work, as the Limelight theme won an Academy Award for Best Original Score in 1973 following the film's re-release.
https://www.youtube.com/watch?v=w4YnJr6OE6A
Here's the Everly Brothers