A year has passed since Matthew said goodbye to his alien friend, and in the summer holidays he meets Albertine, a mathematical prodigy, with whom he discovers he can communicate telepathically. One day Chocky returns to warn Matthew that they are both in danger. When he returns to tell Albertine, he finds she has disappeared.

Chocky hopes, with Matthew and Albertine's help, to help the human race discover cosmic power, which unlike Earth's finite natural resources, will sustain them for as long as the universe itself exists. But their knowledge has aroused a great deal of interest from the military, and they are willing to take drastic action if they don't get what they want.