Space Alien Chase is the storybook segment from the episode: The Moon Rocks!
Oona and Deema pretend to be aliens on Outer Space looking for a place to take a nap but a giant space monster keeps following them! They try to hide on Mercury, but its too hot and they try Neptune, but its too scold. After they leave Neptune, they come across Earth, which is just right! The monster arrives again but Deema, being in no mood asks him what the problem is. He reveals that he was sleepy too and had wished to nap with them in the perfect spot. So they all sleep together as the story ends...