Chaplin was born in the United States but grew up in Switzerland. As a teenager, she appeared as an extra in her father's last film, A Countess from Hong Kong (1966). Her father also wanted her to star in the main role of a winged girl found from the Amazonian rainforest in his next planned film, The Freak, in 1969. However, the project was never filmed because of his declining health and because Chaplin eloped with the French actor Jean-Baptiste Thiérrée.
Chaplin and Thiérrée had first come into contact after he read about Chaplin's aspiration of becoming a circus clown in a magazine article of her father, and asked her to form a new type of circus with him. Soon after their elopement they briefly appeared as two clowns in Federico Fellini's The Clowns (1970), and the next year performed for the first time with the contemporary circusLe Cirque Bonjour, which they had founded together, at Festival d'Avignon. In 1974, they founded a new, smaller circus, Le Cirque Imaginaire, which centered only on their, and occasionally their children's, performances, and from 1990 onwards have performed under the name Le Cirque Invisible.
Chaplin and Thiérrée have two children, Aurélia Thiérrée, (born 24 September 1971), and James Thiérrée, (born 2 May 1974), who are also performing artists. In addition to performing in Le Cirque Invisible, Chaplin has also helped in creating her children's shows, and in 2006 was awarded the French national theatre prize, the Molière Award, for designing the costumes for her son's show, The Junebug Symphony.