After Angelica convinces Chuckie that he's ugly, he takes a cue from the caterpillar and wraps himself in a cocoon, hoping he'll emerge as a cuter kid. - Description from Klasky Csupo.
The babies are watching a butterfly come out of the cocoon while the grownups are watching Dil and Tommy. Chuckie's doing somersaults but goes unnoticed, so Angelica informs him that he has grown out of being cute, then starts dancing. Stu gives the babies ice blocks which Chuckie refuses for fear of getting it on his face. Then he decides to wrap himself uo in a cocoon of blankets, not to turn into a butterfly but to be cuter. He has a dream where he turn into some sort of butterfly hybrid called a Chuckerfly and when he wakes up, people are noticing him but not Angelica, so she tries to cocoon herself too.
Another Klasky Csupo cartoon, Santo Bugito, had a character named Miguel who sat silently waiting to hatch from his cocoon. He never did through the run of the show.
When Tommy is explaining to his friends how caterpillars (referred to by the babies as "kitty-pillars") turn into butterflies, they initially mispronounce it as "butler-fly." But afterward, they correctly pronounce it as "butterfly."