According to Aloys Fleischman, ed., Sources of Irish Traditional Music c.1600-1855, 2 vols. (Garland, 1998; all the tunes are notated in this book), "The Three Captains" (vol.1, no. 3062) was included in John Lee's Collection of Country Dances for the Present Year 1791 (Dublin, 1791). This record, which The Fiddler's Companion doesn't mention, seems to be the earliest. The tune (6/8) is similar to the one (2/2) in O'Neill's Music of Ireland, though there're diferences.

~Masato