It's Matthew's birthday and the family have gone to London. They go on an open-top bus and visit the planetarium. Matthew explains that he wants to be an astronaut when he grows up. It is discovered that Matthew has been adopted. In Maths the following morning, a blue-white light appears and enters the classroom. It seems to be searching for someone. It lands on Matthew and Matthew immediately finds that he can solve the problems straight away, when he couldn't before. Matthew's parents notice his unusual behaviour as he starts to ask some unusual questions. Matthew has a fever and starts talking aloud. His parents discover Chocky, who seems to be an imaginary friend.

The next morning, Matthew's temperature has lowered and he returns to school. His mum is still concerned about him. At school, Matthew has a biology lesson and he asks his teacher, Miss Blayde, about reproduction in a single sex species. Later, his dad gets a new Citroen car. Everyone is excited, but Matthew stands next to the car in a terrible, distressed state. Chocky finds the car stupid and old-fashioned and hates it. At the next Maths lesson, Matthew starts using the binary code to count as that is what Chocky uses. He uses Y and N, for Yes and No, instead of 0 and 1. Matthew plays an electronic game with his friend Colin. When it is Matthew's go, Chocky is curious and she makes the screen explode.

The family go for a picnic beside a river. Chocky is interested about how boats float and Matthew finds a boat and investigates without the owners permission and without telling his parents. The boat owner thinks he has caught a thief and hands Matthew over to a policeman. His dad goes looking for Matthew and finds him with the policeman. Dad's old friend, Dr. Roy Landis comes to see Matthew to speak about Chocky. Landis discovers that Chocky is real and not imaginary. In bed, Matthew finally sees Chocky as a form of a swirly misty hologram

It is the summer holiday for Matthew and Polly. Matthew's mum is tidying up Matthew's bedroom when she finds some strange art work. Matthew admits painting these but in the eyes of Chocky. Matthew is miserable as Chocky has deserted him for his holiday. They meet up with Colin and his family. The children are playing near the river when a boat breaks free and starts to drift downstream. Emma screams which alerts Polly and Matthew. The jetty is destroyed by the impact and Polly and Matthew fall into the water