The elegibunnymonkeybutterduck is an imaginary animal devised by Dr. Nobel Price in Episode 1832 of Sesame Street, named such after the assorted animals that make up its physical being - the body of an elephant, neck of a giraffe, ears of a bunny, tail of a monkey, wings of a butterfly, and head of a duck.
Dr. Price is under the presumption that the animal is real and spends the episode trying to catch it with a butterfly net. He later attempts a trap using the creature's favorite food as bait - a peanut butter, carrot, banana, and flower sandwich (on rye bread).
Gordon and David observe his odd behavior and believe the scientist is going to be let down when yet another of his scientific pursuits ends in failure. They stitch together parts from other animal toys to make a stuffed elegibunnymonkeybutterduck, which Dr. Price only momentarily believes is real. While slightly disappointed that his search was for an animal that only existed in his mind, he's happy to play with his new toy.