"That's All Right" is the name of the first commercial single released by Elvis Presley, written and originally performed by blues singer Arthur Crudup. Presley's version was recorded on July 5, 1954, and released on July 19, 1954 with "Blue Moon of Kentucky" as the B-side. It is #113 on the 2010 Rolling Stone magazine list of the "500 Greatest Songs of All Time".

During an uneventful recording session at Sun Studios on the evening of July 5, 1954, Presley, Moore, and Black were taking a break between recordings when Presley started fooling around with an up-tempo version of Arthur Crudup's song "That's All Right, Mama". Black began joining in on his upright bass, and soon they were joined by Moore on guitar. Producer Sam Phillips, taken aback by this sudden upbeat atmosphere, asked the three of them to start again so he could record it.

Sam Phillips gave copies of the record to local disc jockeys Dewey Phillips (no relation) of WHBQ, Uncle Richard of WMPS, and Sleepy Eyed John Lepley of WHHM. On July 7, 1954, Dewey Phillips played "That's All Right" on his popular radio show "Red, Hot & Blue". On hearing the news that Dewey was going to play his record, Presley went to the local movie theater to calm his nerves.

Interest in the record was so intense that Dewey reportedly played the record 14 times and received over 40 telephone calls. Presley was persuaded to go to the station for an on-air interview that night. Unaware that the microphone was live at the time, Presley answered Dewey's questions, including one about which high school he attended: a roundabout way of informing the audience of Presley's race without actually asking the question.