I first became aware of this song in junior high school when it was featured on an episode of The Partridge Family (my little brother said at the time, "I can't believe you've never heard that one before!"). It was written by Alabama native Hugh Martin for the movie, Meet Me in St. Louis, and was sung by Judy Garland in that movie. Don Williams has a great essay on the two versions of this song: the one used in the movie and the one that has become a popular Christmas song. You can read Don’s essay here. Below you can listen to Frank Sinatra’s version of the song. The original, sung by Judy Garland can be viewed here.
Hugh Martin, by the way, is now 96 years old and living in Encinitas, California.