Billy Corgan developed this song as a result of some encouragement from drummer Mike Byrne. He recalled to MusicRadar.com: "We were recording drums for something else, and there was a problem with the snare drum. I had 10 minutes where I was just standing there with a guitar around my neck, so I started playing a riff. Mike just went, 'Oh, man, I love that riff!' I was like, 'Really?' So to be a show-off, I quickly arranged it into a song. Mike was all for it, and within a week we were recording it."
The Chimera is an androgynous mixed animal creature found in Homer's The Iliad. Homer describes it as: "a thing of immortal make, not human, lion-fronted and snake behind, a goat in the middle, and snorting out the breath of the terrible flame of bright fire." The term chimera has come to describe any mythical animal with parts taken from various animals and, more generally, an impossible fantasy.