  When a compact object is formed, an impulse (kick) will be imparted to the
system by the mass lost during the core-collapse supernova (SN). A number of
other mechanisms may impart an additional kick on the system, although evidence
for these natal kicks in black hole systems remains limited. Updated Gaia
astrometry has recently identified a number of high peculiar velocity (in
excess of Galactic motion) compact objects. Here, we focus on the black hole
low-mass X-ray binary H 1705--250, which has a peculiar velocity
$\upsilon_{\mathrm{pec}}\,=\,221^{+101}_{-108}\,\mathrm{km}\,\mathrm{s}^{-1}$.
Using population synthesis to reconstruct its evolutionary history (assuming
formation via isolated binary evolution within the Galactic plane), we
constrain the properties of the progenitor and pre-SN orbit. The magnitude of a
kick solely due to mass loss is found to be
$\sim\,30\,\mathrm{km}\,\mathrm{s}^{-1}$, which cannot account for the high
present-day peculiar motion. We therefore deduce that the black hole received
an additional natal kick at formation, and place limits on its magnitude,
finding it to be $\sim\,295\,\mathrm{km}\,\mathrm{s}^{-1}$ (minimum
$90\,\mathrm{km}\,\mathrm{s}^{-1}$). This furthers the argument that these
kicks are not limited to neutron stars.
