Information
Authors
Code by John O'Brien aka JOBBEEE https://www.mobygames.com/person/28679/john-obrien/
Graphics by Bill Harbison aka BILL aka Harbonaut https://www.mobygames.com/person/31804/bill-harbison/
Music by Jonathan Dunn aka JON DUNN https://www.mobygames.com/person/31702/jonathan-dunn/
Alternative versions
There's a demo version of Chase H.Q. on Sinclair User issue 94: Megatape 23. https://worldofspectrum.org/archive/software/cover-tapes-and-electronic-magazines/sinclair-user-issue-94-megatape-23-sinclair-user. It features a single stage, with the graphics from stage 1 of the real game and what seems to be a custom map. There's no retry on fail and it's a tough level.
Related ports
The Amstrad CPC version is by the same authors and was produced after this Spectrum version.
Related games
WEC Le Mans (Imagine, 1989) [Lamb/Mullins/Dunn/Harbison/Morrall]
Shares a composer and an artist with ZX Chase H.Q.
https://www.mobygames.com/game/15167/wec-le-mans-24/
Chase H.Q. is reportedly a modification of WEC Le Mans' game engine.

Batman: The Movie (Ocean Software, 1989) [Lamb/O'Brien/Shortt/Drake/Harbison/Palmer/Hemphill/Dunn/Cannon]
ZX Chase H.Q.'s authors worked on the driving sequences for the Atari ST and Amiga versions of this game.
https://www.mobygames.com/game/3848/batman/

Burnin' Rubber (Ocean Software, 1990) [O'Brien/Hemphill/Dunn]
A later Amstrad game by John O'Brien very much like WEC Le Mans.
https://www.mobygames.com/game/70894/burnin-rubber/

Research
https://en.wikipedia.org/wiki/Chase_H.Q.
https://spectrumcomputing.co.uk/entry/903/ZX-Spectrum/Chase_HQ
https://www.mobygames.com/game/9832/chase-hq/
http://reassembler.blogspot.com/2012/06/interview-with-spectrum-legend-bill.html
https://news.ycombinator.com/item?id=8850193 (discussion about the game loader)
http://www.extentofthejam.com/pseudo/ (Lou's Pseudo 3D page)
48K/128K version differences