It's Matthew's birthday. The family have been to the planetarium on a day out in London. At the end of the astronomy show, the family plus Colin (Matthew's best friend) have a ride on an open top London double decker bus. While they travel through the center of London, Matthew plays with a Rubik's cube but cannot solve the problem. Matthew explains to everyone that he wants to be an astronaut when he grows up, Colin wants to be a racing driver. Dad explains that good astronauts have to be good at maths and that Matthew's last school report was not very good. There is also a good indication that he is particularly poor at mathematics. Back at home it is bedtime as it is school in the morning. Matthew is still very excited and wants to read but his mum refuses to allow him. We also learn that Matthew is an adopted child.
The next morning at school Matthew and the rest of the pupils are in class learning about factors. Mr. Trimble is the teacher of mathematics. The teachers sets out some problems on the chalk board and asks the pupils to quietly solve them. Everyone's head goes down and they start to work on the numbers. Suddenly at one of the classroom windows a blue white light appears and enters the class room. None of the pupils seem to notice it as it moves from one child to another. For some reason it appears to be looking for someone as it tries several children before rejecting them. The light eventually lands on Matthew. At first Matthew thinks someone in the class has called his name but he then finds that he can solve all the maths problems when before he would have found them too difficult. Matthew then asks "what" which disturbs the teacher. Matthew states that he has finished the problems. The teacher does not really believe him and asks him to bring out his work the the front desk. Mr. Trimble checks his answers and agrees that he has completed all the problems, much to the envy of the other members of the class.
It becomes pretty apparent that Matthew has changed since his birthday. He starts asking lots of unusual questions which his parents have difficulty in answering. This causes them great concern especially when he starts talking to himself. On several occasions his dad hears him talking to no one about time and periods of the day and year. Both Matthew's mum and his dad have noticed this unusual behaviour. Later that night Matthew is not at all well. He is running a fever and is very tired but cannot go to sleep. He keeps asking Chocky to stop talking. He is very restless and cannot sleep as Chocky keeps on asking questions and does not seem to understand about illness. Eventually Matthew asks his mum to make Chocky shutup and stop bothering him. His mum does not believe what is going on but in order to calm him she speaks to Chocky and Matthew settles down for a good night's sleep. His mum and dad are really worried now. We also get to learn that Chocky is referred to as a "he" although later Chocky becomes a "she." His parents decide that it may be another Piff, which is the name of the imaginary friend of Polly (Matthew's sister).