Allan Stuart Chase was born June 22, 1956, in Willimantic, Connecticut, and moved with his family to Phoenix, Arizona, at age four. He started alto saxophone in 1965, at nine, encouraged by a family friend, the jazz pianist and vocalist Karl Woodman, and went on to earn a bachelor's degree in music theory and composition from Arizona State University in 1978. He then spent a year in graduate jazz performance study at the New England Conservatory (1980-81) before returning to Boston-area music full time.

Chase's most consequential teacher was pianist Jaki Byard, with whom he studied at Berklee College of Music, where Chase joined the faculty in 1981 and taught until 1990 (he later returned as Ear Training department chair from 2008 to 2021, retiring from the school in May 2026). He also studied at the Creative Music Studio with Anthony Braxton, Roscoe Mitchell, Karl Berger, and George Lewis, and earned a master's degree in ethnomusicology from Tufts University in 1988 with a thesis on the music of Sun Ra. In 1981 he co-founded Your Neighborhood Saxophone Quartet, a cooperative reeds-only group that stayed together until 1995 (with periodic reunions after 2006), recording six albums for the Belgian label Coppens and Your Records and completing ten European tours; its best-known release, Plutonian Nights: The Music of Sun Ra (1991), drew directly on the research behind his Tufts thesis.

In 1992 Chase joined drummer Rashied Ali's downtown New York quintet Prima Materia, formed to perform the late repertoire of John Coltrane and Albert Ayler at full length. He stayed with the band through 2000 and appears on all four of its albums: Peace on Earth (Music of John Coltrane) (1994, with John Zorn guesting on two tracks), Meditations (1995) and Bells (1996), both recorded live at the Knitting Factory, and the posthumous Configurations (The Music of John Coltrane) (2009). For Bells, Chase personally transcribed Ayler's 1965 original from the record so the quintet could rework it as a single continuous performance. The group also played the 1997 Vision Festival, documented on AUM Fidelity's Vision Volume One, and the 1996 North Sea Jazz Festival.

Chase led his own working quartet from 1995, with trumpeter Ron Horton, bassist Tony Scherr, and drummer Matt Wilson, recording the debut Dark Clouds with Silver Linings (Accurate Records, AC 5013, 1995), an album of standards and originals that the group's own liner notes describe as indebted to the pianoless two-horn quartets of Sonny Rollins and Gerry Mulligan. A second leader session, Phoenix (Jazz Project Recordings, JP2001), followed with Lewis Nash on drums, David Finck on bass, Ron Horton again on trumpet, and Adam Kolker on reeds; Discogs dates its release to 1999, though Chase's own account of the record places its recording closer to the mid-1990s. Beyond his own leader dates, Chase's discography as a soloist runs past sixty recordings, including sessions with composer Gunther Schuller, vocalist Dominique Eade (his wife, also an NEC faculty member), bassist Joe Morris, and pianist Stanley Cowell, plus sideman work with drummer Alan Dawson, bassist Teddy Kotick, guitarist Mick Goodrick, and pianist Fred Hersch.

Chase's academic career ran alongside his playing. He taught at Tufts University from 1993 to 1997 and at the New England Conservatory from 1994 to 2012, chairing NEC's jazz studies and improvisation department (1996-2001) and its contemporary improvisation department (2005-2008), and serving as the school's dean of faculty from 2000 to 2006; he returned to NEC's faculty in 2023 and continues teaching graduate courses there. In parallel, he kept recording: the Bruno Råberg trio albums For the Unknown (2015, with trumpeter Phil Grenadier) and The Prospector (2020, with drummer Austin McMahon), Shamanic Soliloquies (2018) co-led with drummer Ra-Kalam Bob Moses, regular work with the Steve Lantner Quartet and the Joe Morris Bass Quartet, and (Embodied) | (Ephemeral), a trio session with pianist Jed Wilson and drummer Tony Falco recorded August 27, 2022, and released September 1, 2023. He remains active in 2026, performing on the New England Jazz Collaborative's debut album Tributaries (ACP Records, released July 17, 2026) and appearing, per Spotify's own catalog data, on a further 2026 quartet session titled Itineraries of Escape with Falco, Wilson, and reedist Josh Sinton (a session not yet corroborated by any secondary press source at the time of this profile).

Chase's playing sits at the intersection of two traditions he never treated as opposites: the freely structured, full-length repertory readings he helped Rashied Ali's Prima Materia build around Coltrane's and Ayler's most demanding late compositions, and a harmonically grounded, blues- and bebop-rooted mainstream voice audible on his own quartet records and in decades of sideman work. His Tufts thesis on Sun Ra's music and his years studying with Anthony Braxton, Roscoe Mitchell, and Jaki Byard fed both sides of that split, and as chair of jazz studies and later contemporary improvisation at the New England Conservatory, and as Berklee's longtime ear-training department head, he shaped how a generation of Boston-trained improvisers were taught to think about the same range of material. AllMusic's Chris Kelsey singled him out, alongside tenor saxophonist Louie Belogenis, for "remarkable strength and control" fronting Prima Materia against Ayler's Bells; JazzTimes praised the same performance in 1997. His transcription of Bells directly from Ayler's original recording, done so the quintet could perform it as a single 65-minute piece, is emblematic of an approach that treats free jazz's canon as repertoire to be studied and re-read rather than simply gestured at.