  We report the discovery of two well-defined tidal tails emerging from the
Hyades star cluster. The tails were detected in Gaia DR2 data by selecting
cluster members in the three-dimensional galactocentric cylindrical velocity
space. The robustness of our member selection is reinforced by the fact that
the sources depict an almost noiseless, coeval stellar main sequence in the
observational Hertzsprung-Russel diagram. The spatial arrangement of the
selected members represents a highly flattened shape with respect to the
direction of movement along the clusters' orbit in the Galaxy. The size of the
entire structure, within the limits of the observations, measures about 200 pc
in its largest extent, while being only about 25 pc thick. This translates to
an on-sky extent of well beyond 100 deg. Intriguingly, a top-down view on the
spatial distribution reveals as distinct S-shape, reminiscent of tidal tails
both observed for globular clusters, as well as modelled for star clusters
bound to the Galactic disk. Even more remarkable, the spatial arrangement, as
well as the velocity dispersion of our source selection is in excellent
agreement with previously published theoretical predictions for the tidal tails
of the Hyades. An investigation into observed signatures of equipartition of
kinetic energy, i.e. mass segregation, remains unsuccessful, most likely due to
the sensitivity limit for radial velocity measurements with Gaia.
