Written and first recorded by Shel Silverstein (1962).
Hit version by The Irish Rovers (US #7/MOR #2/IRE #5 1968).
From the wiki: “‘The Unicorn Song’ was written and first recorded by Shel Silverstein in 1962, released in 1962 on his album Inside Folk Songs, and made very popular by Canadian band The Irish Rovers in 1968. The song tells that unicorns were not a myth but a creature that literally missed the boat, not boarding the Ark in time to be saved from the Great Flood. It remains one of the best-known songs of the The Irish Rovers’ long career.
“In the original recording of the song, The Irish Rovers speak half of the lyrics; on the remakes, the majority of the song is sung – except for the final line, which is also spoken freely, without the music. Will Millar of The Irish Rovers recorded another, earlier version of the song with the St. Michaels Kids. In 1981, Millar opened an Irish pub in Toronto, Ontario, under the name The Unicorn.”
The Irish Rovers, “The Unicorn Song” (1968):