A female prophet or fortune-teller.
Example:
Her mother treated her as if she were the family sibyl, able to predict what fate was about to befall her sisters.
The sibyls were ancient prophetesses who lived in Babylonia, Greece, Italy, and Egypt. The most famous was the Sibyl of Cumae in Italy, a withered crone who lived in a cave. Her prophecies were collected into twelve books, three of which survived to be consulted by the Romans in times of national emergencies. Whether or not she was the first sibyl, her name or title became the term for all such prophets.