Star Platinum

High in the heavens, there was a girl who was training in a shrine to be the successor of a goddess. One day, the goddess had to leave the shrine to attend a meeting of the many gods, leaving the girl alone at the shrine. The goddess warned her to leave alone a box of star-souls within the shrine, and that under no circumstances should she open it. Naturally, as soon as the goddess had left, the girl's curiosity got the better of her and she opened the box.

The star-souls escaped, turned the girl into a small fairy, and fled down towards the Earth. She must track down and capture the star-souls, now causing mischief on Earth, before the goddess returns to the shrine. However, while chasing several of the star-souls through the sky, the girl crashes through the window of a young man who lives on Earth. She decides that since he can somehow see her, that he's going to help her out, and so the two of them begin their adventure.

[From Mobygames]