An unnamed teenager spends one summer with his parents on an island in New England. He spends most of his time riding his bicycle down to the neighbor's house, where a girl named Billie lives. He picks her up each morning, and they spend each day together. The boy is infatuated with Billie to the point of obsession. In the evenings, he rides home.

A stranger begins visiting the boy's every few days. This visitor talks very little, mainly listening to the boy's father tell stories about his youth. The boy thinks this stranger is detached and independent, never emotionally involved in anything outside of himself. For this reason, he does not like the visitor.

When the summer draws to an end, the island community always holds a masquerade ball. This is the first year that Billie and the boy are old enough to attend. On the night of the party, while the boy and his family dress up in fancy costumes, the visitor comes dressed plainly in an ordinary suit, upsetting the boy's mother. They all go to the ball, where the boy sees Billie talking to a group of other men. The boy tries to approach her, but she starts dancing. When he is finally able to cut in, she greets him as if he were any other man. Shortly after, someone else cuts in on him.

The boy spends most of the night chasing Billie, hoping to get close to her. At one point, the visitor, standing off to the side, beckons him over and asks him why he is not dancing very much. The boy replies that he has not seen the visitor dance at all. The visitor says that he is in danger. When asked why he is not wearing a costume, the visitor says that he is wearing one, and it is meant to protect against the danger. The boy gets distracted when he sees Billie again, and he wanders off, even though he knows that he has lost her.