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.

Accepted to MNRAS; 16 pages