Co-written (by Bobby Darin) and first recorded by The Ding Dongs (1958).
Hit version by The Rinky Dinks (US #24/R&B #8 1958), Buddy Holly (US #32/UK #17 1958).
From the wiki: “‘Early in the Morning’ was written by Bobby Darin and Woody Harris. Darin, a member at the time of the Brill Building gang of struggling songwriters, approached Brunswick Records with the song; Brunswick was impressed, but as Darin was still under contract to Atlantic Records’ subsidiary, Atco, the song was released as by ‘The Ding Dongs’ (in reality, Bobby Darin and backing vocalists). New York deejays liked the record but Atco soon discovered the deception. Brunswick was forced to turn over the masters to Atco, who re-released the record in 1958 under the name ‘The Rinky Dinks’. A version by Buddy Holly competed in the UK with Darin’s single, which was released there under Darin’s own name.”
The Rinky Dinks, “Early in the Morning” (1958):
Buddy Holly, “Early in the Morning” (1959):