As to the song itself, "That'll Be the Day" was written by Buddy Holly and Jerry Allison (the drummer for The Crickets). It took its title from a line used by John Wayne as Ethan Edwards repeatedly in the movie The Searchers, "That'll be the day." Here it must be noted that The Searchers would not only inspire the song "That'll Be the Day" by The Crickets. The film's title would would also serve as the inspiration for the name of British Invasion era Liverpudlian band The Searchers.
Here, then, is "That'll Be the Day" by The Crickets