Pick Your Pet is a game show from the first season of Sesame Street, and is a parody of The Dating Game. It is the show's very first game show segment.
Pick Your Pet is hosted by Guy Smiley, who was, at this point, named Sonny Friendly. The Pick Your Pet contestant wears a blindfold while questioning three different animals; from among them, she will choose her pet. The contestant in this skit is Lucy Jones (who would later become Betty Lou), and the animal choices are a bird (Little Bird), a dog (Baskerville), and a monster (Beautiful Day Monster), the last of which Sonny considers hideous and doesn't think the contestant would want.
Lucy asks the animals a series of questions that indicate she hopes she'll be able to choose a cat. Her time runs out before she can ask Beautiful Day Monster any questions. She has to choose, so she picks Beautiful Day Monster. The monster acts like a cat, so Lucy is happy with her pet.