Joan Chissell was born in Cromer, Norfolk, and educated at the Manor School in Sheringham. In 1937, she won a scholarship to the Royal College of Music, where she studied piano, composition, music history, and criticism. Her performing career was cut short by a hand injury. While still a student at the RCM, she gave the first performance in the UK of Maurice Ravel's Piano Concerto for the Left Hand. She began to teach at the RCM in 1943, and went on to the faculties of Oxford University and the University of London. She joined The Times of London as the first female music critic in 1948, a post she held for more than 30 years, until her retirement in 1979. She also contributed articles to The Gramophone magazine and regularly broadcast programs for the BBC.
She specialized in the works of Robert Schumann and wrote two books about him. In 1991, for her contributions to Schumann's legacy, she won the Robert Schumann Prize awarded by the city of Zwickau, his birthplace. Ms. Chissell also wrote books about Clara Schumann, the couple's friend Johannes Brahms, and Frédéric Chopin. She served as a juror at international music competitions, including the Sydney International Piano Competition in 1988 and 1992. The Joan Chissell Schumann Prize, a major piano competition at The Royal College of Music, was established in her memory.