In Greek mythology, the chimera was a female monster with the head of a lion, the torso of a goat, and the tail of a snake. An alternative spelling (mostly British, according to Webster’s) is chimaera. When in doubt, ask the monster which spelling she prefers.
This is from Borges’ “Book of Imaginary Beings” tr. Hurley:
The commentator Servius Honoratus has observed that all authorities agree that the monster came originally from Lycia, where there is a volcano that bears its name. The base of the volcano is infested with serpents; on its sides there are meadows where goats pasture; and on the top, flames shoot forth and lions have their dens. The Chimaera might, then, be a metaphor for that wonderful mountain. Earlier, Plutarch had suggested that “ChimAera” was the name of a ship’s captain with tendencies toward the piratical; he had painted a lion, a she-goat, and a snake on his ship.
These absurd conjectures prove that people were already growing quite tired of the Chimaera. It was better to translate the beast into something (anything) else than to picture it as it was. It was too heterogeneous; the lion, the she-goat, and the serpent (in some texts, the dragon) resisted merging into a single animal. In time, the fearsome Chimeara became “chimerical”; a famous quip by Rabelais (who asked whether a Chimaera, bobbing about in the void, would eat puns) is perhaps the watershed. The incoherent shape fades away and the word remains, to stand for “the Impossible.” “An illusion or fabrication of the mind” is the definition one finds in the dictionary today.
The chimera's story has given rise to another fun coinage. The chimera was wreaking havoc in the country of Lycia, and King Iobates was looking for a hero to destroy her. The handsome and brave Bellerophon arrived in the kingdom with a letter of introduction to Iobates from the king's son-in-law. Unfortunately, the son-in-law was jealous of Bellerophon, so the letter went pretty much as follows:
Dear King Iobates,
Please kill the bearer of this letter.
Iobates sent Bellerophon to battle the chimera, thinking this would surely kill him, but the hero triumphed with the aid of the horse Pegasus. Ever since, the term “Bellerophontic letters” has been used to describe any kind of communication that a person is made to carry, containing matter prejudicial to himself.