The Star of Cottonland

Tokio, a student who couldn't take his university entrance exams due to a cold, finds a weakened kitten on the street and takes her home. Tokio's mother is allergic to cats, but seeing how her son is invigorated by the feline, she can't help but permit him to keep the pet. Simply called Chibi Neko by her new owner, the kitten is fascinated by the world around her.

Synopsis from Anime News Network