  We report the discovery of a wide co-moving substellar companion to the
nearby ($D=67.5\pm1.1$ 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
$525\pm125$ 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$5\pm2$), at a temperature of $1650\pm200$ K.
Combining the measured near-infrared magnitude of $\zeta$ Del B with the
estimated temperature leads to a model-dependent mass estimate of $50\pm15$
M$_{\rm Jup}$, corresponding to a mass ratio of $q=0.019\pm0.006$. At a
projected separation of $910\pm14$ 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.
