She was born in 1798 in Brislington, near Bristol, the second child and only daughter of Mary Jane Vial Clairmont. Throughout her childhood, she was known as "Jane". In 2010 the identity of her father was discovered to be John Lethbridge (1746–1815, after 1804 Sir John Lethbridge, 1st Baronet) of Sandhill Park, near Taunton in Somerset. Her mother had identified him as a "Charles Clairmont", adopting the name Clairmont for herself and her children, to disguise their illegitimacy. It appears that the father of her first child, Charles, was Charles Abram Marc Gaulis, "a merchant and member of a prominent Swiss family, whom she met in Cadiz".
In December 1801, when Clairmont was three years old, her mother married a neighbour, the writer and philosopher William Godwin. This brought her two stepsisters: Godwin's daughter Mary (later Mary Shelley), only eight months her senior, and his stepdaughter Fanny Imlay, a couple of years older. Both were the daughters of Mary Wollstonecraft, who had died four years before, but whose presence continued to be felt in the household. The new couple soon became the parents of a son, Claire's youngest sibling.
All of the children were influenced by Godwin's radical anarchist philosophical beliefs. Both parents were well-educated and they co-wrote children's primers on Biblical and classical history. Godwin encouraged all of his children to read widely and give lectures from early childhood.
Mary Jane Clairmont was a sharp-tongued woman who often quarrelled with Godwin and favoured her own children over her husband's daughters. She contrived to send her volatile and emotionally intense daughter to boarding school for a time, thus providing her with more formal education than her stepsisters. Unlike Mary, Claire Clairmont was fluent in French as a teenager; later she was credited with fluency in five languages. Despite their different treatment, the girls grew close and remained in contact for the rest of their lives.
At sixteen Clairmont was a lively, voluptuous brunette with a good singing voice and a hunger for recognition. Her home life had become increasingly tense as her stepfather William Godwin sank deeper into debt and her mother's relations with Godwin's daughter Mary became more strained. Clairmont aided her stepsister's clandestine meetings with Percy Bysshe Shelley, who had professed a belief in free love and soon left his own wife and two small children to be with Mary. When Mary ran away with Shelley in July 1814, Clairmont went with them. Clairmont's mother traced the group to an inn in Calais but couldn't make Clairmont go home with her. Godwin needed the financial assistance that the aristocratic Shelley could provide.