According to About.com, the song "Jolly Old Saint Nicholas" was initially published anonymously. Historians often attribute authorship of the song to Benjamin Hanby. Some people also credit singer Wilf Carter, also known as Montana Slim, with writing the song, because he was the first to record it.
About.com notes that Carter could not have been the author of "Jolly Old Saint Nicholas" because the song was published in its written form before Carter recorded it. Hanby is thought to be the author because of the similarities between the song and "Up on the Housetop," another Christmas song he wrote that was published around the same time. Hanby was also a pastor and school principal.