Like many characters in Sailor Moon, Chibi Chibi's background and characterization vary greatly depending on the medium. In the Manga, she was a disguised form of Sailor Cosmos (who was in turn strongly implied to be a future version of Sailor Moon). In the 90's Anime, she was the star seed or "Soul" of Sailor Galaxia
As she comes from the infinitely endless cosmos itself, Eternal Sailor Chibi-Chibi's magical powers are likely infinitely limitless and god-like. One shown ability was teleporting herself and others across vast distances in a flash of bright pink glowing light. This great power seems to take a lot out of her as she often sleeps after using this ability. Her other magical powers and attacks are unknown, but seem to come from her heart-shaped mystical scepter. She was once able to block Sailor Galaxia's "Galactica Super String" attack, a sign that she is an extremely powerful character indeed.