ABSTRACT 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 ∼2.35 M⊙ A-type star located at a distance of ∼9 kpc from the Sun and has a heliocentric radial velocity of 1017 ± 2.7 $\mathrm{\, km\, s^{-1}}$ without any signature of velocity variability. The current 3D velocity of the star in the Galactic frame is 1755 ± 50 $\mathrm{\, km\, s^{-1}}$. 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 ∼1800 $\mathrm{\, km\, s^{-1}}$ 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 Vy,⊙ = 246.1 ± 5.3 $\mathrm{\, km\, s^{-1}}$ or position R0 = 8.12 ± 0.23 kpc. The ejection trajectory and transit time of S5-HVS1 coincide with the orbital plane and age of the annular disc 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.