Chobits makes you believe a romance between a boy and a computer could matter. The show's real trick isn't the sci-fi setup, it's that every conversation between Hideki and Chii feels like you're watching two people figure each other out for the first time, even when one of them is literally learning what "love" means from a book. Hideki's emptiness isn't a flaw; it's the whole point. He needs someone to complete him, and Chii needs someone to teach her what she's for. That premise will either feel like the sweetest thing you've ever watched or aggressively hollow, depending on whether you buy that vulnerability in romance at all.
Hideki's broke and desperate for a personal computer. In this future, Persocoms are everywhere: humanoid machines that handle daily tasks, obey commands, fit seamlessly into society. When he stumbles across a discarded one on the street, he can't believe his luck. He takes her home, powers her up, and gets nothing but a confused "Chii" in response. So that's what he names her. As Hideki teaches Chii about the world, something strange happens. She learns faster than any Persocom should. She expresses emotions that shouldn't exist in artificial beings. She seems almost human, which shouldn't be possible. The more time they spend together, the clearer it becomes: Chii might be a Chobit, a mythical type of Persocom with genuine consciousness and free will. If she really is, then everything about her existence breaks the rules. And Hideki's feelings for her start breaking rules too.