"Time Is on My Side" is a song written by Jerry Ragovoy. First recorded by jazz trombonist Kai Winding and his orchestra in 1963, it was covered by both soul singer Irma Thomas and then later the Rolling Stones in 1964.

Kai Chresten Winding was a Danish-born American trombonist and jazz composer. He is known for his collaborations with fellow trombonist J. J. Johnson. His version of "More", the theme from the movie Mondo Cane, reached in 1963 number 8 in the Billboard Hot 100 and remained his only entry here.