Nichols' youth was difficult because by age 4, following an inoculation for whooping cough, he had lost his hair, and consequently wore wigs and false eyebrows for the rest of his life. He became a naturalized citizen of the United States in 1944 and attended public elementary school in Manhattan (). After graduating from the Walden School, a private progressive school on Central Park West, Nichols briefly attended New York University before dropping out. In 1950, he enrolled in the pre-med program at the University of Chicago. He later described this college period as "paradise," recalling how "I never had a friend from the time I came to this country until I got to the University of Chicago."