He was born in Kingsbury, a suburb of northwest London, in England, and was trained in the church choir as a young boy, beginning his musical career in the church's basement. In 1964, he was suspended from school for "having long hair", and given money to get a haircut. Instead he went home, used the money for other things, and never returned to school.

Squire was fond of experimenting with LSD in the 1960s, until an incident where he had a bad acid trip. He recalls that he spent months inside his girlfriend's apartment, afraid to leave, and it was during this time that he learned how to play bass. He recovered and never used acid again.

Squire's early influences were diverse, ranging from church and choral music to the Merseybeat sounds of the early 1960's. Squire's first musical groups The Selfs, The Syn, and later, Mabel Greer's Toyshop, would introduce him to his early Yes collaborators Peter Banks and Jon Anderson and to Andrew Jackman.

During his first conversation with Anderson, the pair broke the ice by discussing one of their favorite bands, Simon & Garfunkel.

Yes released its first record in 1969, and though the band has had many personnel changes over the years, they have continued to record and tour for over 30 years. Squire is the only member who has remained in the lineup throughout the band's tenure.

During the band's formative years Squire was frequently known for his tardiness, a habit that drummer Bill Bruford often complained about. Because of this, Squire would frequently drive at unsafe speeds to get to gigs on time, once causing a horrific accident on the way to a gig in Germany after he fell asleep at the wheel, although miraculously nobody was injured.

As Squire, along with Alan White and Steve Howe co-owned the "Yes" name at the time, the 1989 ABWH lineup without him (which contained Anderson, Bruford, Wakeman and Howe) could not record under that name.

Squire's bass playing is noted for being aggressive, dynamic, and melodic. Squire's main instrument is a Rickenbacker 4001, which he has owned and played since 1965; it was the fourth Rickenbacker 4001 ever imported into Britain from the United States. This instrument, with its warmth and distortion, is a significant part of Squire's unique sound which is achieved by a technique known as 'bi-amping'. By splitting the stereo signal from his bass (which divided the signal from the pickups into dual high and low frequency outputs) and then sending the low frequency output to a conventional bass amplifier and the high-frequency output to a separate lead guitar amplifier, Squire produced a tonal 'sandwich' that added a growling, overdriven edge to the sound while retaining the Rickenbacker's powerful bass response. Squire (who is self-taught) was also one of the first rock bass players to successfully adapt electronic guitar effects such as tremolo, phasing and the wah-wah pedal to the instrument.

Squire's vocals are also key to Yes' music, providing important harmonization with Jon Anderson's distinctive countertenor.

Squire has concentrated overwhelmingly on Yes' music over the years, and his solo works have been few and far between. His first and only true solo record was 1975's Fish Out of Water, featuring Yes alumni Bill Bruford on drums and Patrick Moraz on keyboards and The Syn/The Selfs alumnus Andrew Jackman also on keyboards. Squire was later a member of the short-lived XYZ (eX-Yes/Zeppelin) in 1981, a group composed of Alan White (Yes) on drums and Jimmy Page (Led Zeppelin) on guitar. However, this group quickly disbanded and never released any material. Squire also played a role in bringing Trevor Rabin into the Cinema band project, which became the 90125 lineup. Later, Squire would join with Yes guitarist Billy Sherwood in a side project called Conspiracy. This band's self-titled debut album contained the nuclei of several songs that had appeared on Yes' recent albums. Conspiracy's second album, The Unknown, was released in 2003. In late 2004, Squire joined a reunion of The Syn.

Chris Squire is commonly known by his nickname Fish, and the name is associated with many of his works (for example his solo record, and his solo piece Schindleria Praematurus (The Fish) from the 1972 Yes record, Fragile). The name has a triple origin. First, his astrological sign is Pisces, and he is apparently a believer in astrology. Second, in the early days of Yes career, he once accidentally flooded a hotel room in Oslo, Norway while taking a shower, and Bill Bruford gave him the nickname. He has also acquired this nickname due to the alleged amount of time he spends in the bath tub.