We report the discovery of a wide co-moving substellar companion to the nearby ($D=67.5pm1.1$ pc) A3V star $zeta$ Delphini based on imaging and follow-up spectroscopic observations obtained during the course of our Volume-limited A-Star (VAST) multiplicity survey. $zeta$ Del was observed over a five-year baseline with adaptive optics, revealing the presence of a previously-unresolved companion with a proper motion consistent with that of the A-type primary. The age of the $zeta$ Del system was estimated as $525pm125$ Myr based on the position of the primary on the colour-magnitude and temperature-luminosity diagrams. Using intermediate-resolution near-infrared spectroscopy, the spectrum of $zeta$ Del B is shown to be consistent with a mid-L dwarf (L$5pm2$), at a temperature of $1650pm200$ K. Combining the measured near-infrared magnitude of $zeta$ Del B with the estimated temperature leads to a model-dependent mass estimate of $50pm15$ M$_{rm Jup}$, corresponding to a mass ratio of $q=0.019pm0.006$. At a projected separation of $910pm14$ au, $zeta$ Del B is among the most widely-separated and extreme-mass ratio substellar companions to a main-sequence star resolved to-date, providing a rare empirical constraint of the formation of low-mass ratio companions at extremely wide separations.
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