So... is Chinpui finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: April 18, 1991
Manga finished: February 01, 1991
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Chinpui is a lighthearted animated series adapted from a manga created by F. Fujio Fujiko.
The story revolves around a young girl whose ordinary life is unexpectedly turned upside down by the arrival of Chinpui.
Chinpui, an adorable and somewhat mischievous creature from another planet, is tasked with preparing this girl to potentially become a princess.
As Chinpui guides her through various comical and sometimes challenging situations, the series explores themes of friendship, responsibility, and navigating the unexpected changes that life throws your way.
The anime focuses on the everyday adventures and humorous interactions between the girl, Chinpui, and the people around them, all while hinting at a larger, more whimsical world beyond their own.