Recent theoretical work in celestial mechanics has revealed that an asteroid may orbit stably in the same region as a planet, despite revolving around the Sun in the sense opposite to that of the planet itself(1-5). Asteroid 2015 BZ(509) was discovered(6) in 2015, but with too much uncertainty in its measured orbit to establish whether it was such a retrograde co-orbital body. Here we report observations and analysis that demonstrates that asteroid 2015 BZ(509) is indeed a retrograde co-orbital asteroid of the planet Jupiter. We find that 2015 BZ(509) has long-term stability, having been in its current, resonant state for around a million years. This is long enough to preclude precise calculation of the time or mechanism of its injection to its present state, but it may be a Halley-family comet that entered the resonance through an interaction with Saturn. Retrograde co-orbital asteroids of Jupiter and other planets may be more common than previously expected.