First recorded by The Byrds (1971).
Also recorded by The Nitty Gritty Dirt Band (1972).
Hit album version by Jackson Browne (1972).
From the wiki: “‘Jamaica Say You Will’ (alternately ‘Jamaica, Say You Will’) was written by Jackson Browne, but was first recorded for release by The Byrds on their Byrdmaniax album, produced by Kim Fowley, the year before Browne’s version came out. ‘Jamaica Say You Will’ was also recorded by the Nitty Gritty Dirt Band for their All the Good Times, released the same month as Browne’s self-titled debut album (aka Saturate Before Using) in January 1972.