  We present the serendipitous discovery of the fastest Main Sequence
hyper-velocity star (HVS) by the Southern Stellar Stream Spectroscopic Survey
(S5). The star S5-HVS1 is a $\sim 2.35$ M$_\odot$ A-type star located at a
distance of $\sim 9$ kpc from the Sun and has a heliocentric radial velocity of
$1017\pm 2.7$ km/s without any signature of velocity variability. The current
3-D velocity of the star in the Galactic frame is $1755\pm50$ km/s. When
integrated backwards in time, the orbit of the star points unambiguously to the
Galactic Centre, implying that S5-HVS1 was kicked away from Sgr A* with a
velocity of $\sim 1800$ km/s and travelled for $4.8$ Myr to its current
location. This is so far the only HVS confidently associated with the Galactic
Centre. S5-HVS1 is also the first hyper-velocity star to provide constraints on
the geometry and kinematics of the Galaxy, such as the Solar motion
$V_{y,\odot}= 246.1\pm 5.3$ km/s or position $R_0=8.12\pm 0.23$ kpc. The
ejection trajectory and transit time of S5-HVS1 coincide with the orbital plane
and age of the annular disk of young stars at the Galactic centre, and thus may
be linked to its formation. With the S5-HVS1 ejection velocity being almost
twice the velocity of other hyper-velocity stars previously associated with the
Galactic Centre, we question whether they have been generated by the same
mechanism or whether the ejection velocity distribution has been constant over
time.
