The story centres around the life of Hideki Motosuwa, a poor student (ronin) attempting to get into university by studying at Seki cram school, and in particular his relationship with a persocom (a computer designed to look like a person) called Chii, who is a Chobit (a sort of super-persocom with abilities far in advance of normal Persocoms, most remarkably emotions).
It also deals with the possible future problem (if and when artificial companions become a reality) of people not having time for other people and preferring to spend it with their persocom, and what effect this has on those who want a relationship with another human.
As well as making several interesting points about relationships, the series and the manga also contain quite a bit of humour, mainly centred around Chii's attempts to learn about her environment and ignorance of the usual social norms.
An important piece of the Chobits Story is a series of in-story books, which are written about the main character, called A City With No People.
For those who can read Japanese, the final ツ character is in Katakana instead of Hiragana because this is the user password Hideki gives Chii at the end of the series.Story