Teenager David Clemens (Keir Dullea) develops a hysterical fear that he will die if he comes into physical contact with another person. Perturbed, David's overbearing mother places him in a home for mentally disturbed young people, but David remains withdrawn from the other patients and his psychiatrist. Over time, however, David grows interested in 15-year-old Lisa (Janet Margolin), who suffers from multiple personalities -- one who can only speak in rhyme, and the other, a mute.