That's All Right är Elvis första singel. Låten skrevs och framfördes ursprungligen av bluesartisten Arthur Crudup som "That's All Right, Mama". Elvis version spelades in i juli 1954, och släpptes med Blue Moon of Kentucky på B-sidan.
After an early rendition of the song, Sun Records owner Sam Phillips exclaimed, "BOY, that's fine, that's fine. That's a POP song now!." Presley responded, "That sounds like Carl Perkins!" As with all of the Presley records issued by Sun, the artists were listed as "ELVIS PRESLEY SCOTTY and BILL".
The record was played on Juke Box Jury. "Blue Moon" had been written and first recorded some years earlier by a famous, Grand Ole Opry entertainer, Bill Monroe of Kentucky. Tennessee Ernie Ford, on the Juke Box Jury that night, drawled: "If ole Bill Monroe hears this, he'll just take his li'l ole country band and head back for the hills." Monroe himself, far from being offended, sent Elvis a note of thanks. After Elvis brought it out, six other companies made it with their stars. Billboard gave Elvis' first record an 85 score, very high, on both sides. Over a 15 week period, only one other record in the same category had an equal rating, and that was by the established star, Webb Pierce. A year later Sam Phillips still hadn't figured out which was the big side. "That's All Right" was in the R&B idiom of negro field jazz, "Blue Moon" more in the country field, but there was a curious blending of the two different musics in both. With Presley's version of Monroe's song consistently rated higher, both sides began to chart across the South.