In the future, almost every person roams arounds with persocons, robots that look like humans and act (somewhat) like humans. However, poor Hideki, a cram student doesn’t have the money for his own. He crosses a persocon in the garbage wrapped in bandages. Once he activates her, she only knows the word “Chii.” As each day passes, Hideki finds out more about Chii’s past and in turn Chii learns more about the world.
I recommend reading Angelic Layer before reading this series.