(The recording is at the bottom if you don’t want to read through my crap.)
According to virtuoso pianist/composer/biographer and contemporary Franz Liszt, Chopin wrote this after watching a dog chase its own tail.
Chopin was in the habit of having his students write out his pieces for him. Not having music written in his own hand might make some wonder about the authenticity of certain works. There is no doubt this one is legit; regardless, art is art.
Chopin did not name his works although according to Wikipedia he did name this one (interesting how Wikipedia is a treasure trove of facts except for those things you are genuinely knowledgeable of). His publisher named his pieces in an attempt to make the sheet music more salable. This particular piece was originally published in Germany and titled (in german) “The Little Waltz”. This was translated later into english as The Minute (my-newt) Waltz and given its brevity people mistakenly pronounced it as The Minute (as in 60 seconds) Waltz.
While the demeanor of this piece is labeled “molto vivace” meaning “very lively” I do not choose to play it prestissimo (as fast as possible) as so many do. Instead I play it at a more stately tempo intending to bring out the various qualities of the music rather than demonstrating brash technique. It is after all a waltz, not a conniption.