Chimera

chimera, n. ("kai meer uh") 1. in general usage, an imaginary monster compounded of incongruous parts, such as a unicorn or a griffin. 2. specifically, in Greek mythology, a fire-breathing she-monster having a lion's head, a goat's body, and a serpent's tail. 3. in D&D, a monster with the hindquarters of a goat, the forequarters of a lion, and three heads; one goat, one lion, and one dragon. [GJ1]
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Addendum: Never pronounced "shimmer-uh." [GJ1]