Hyper-velocity stars (HVSs) were first predicted by theory to be the result of the tidal disruption of a binary system by a super-massive black hole (SMBH) that accelerates one component to beyond the Galactic escape velocity (the Hills mechanism). Because the Galactic centre hosts such a SMBH it is the suggested place of origin for HVSs. However, the SMBH paradigm has been challenged recently by the young HVS HD 271791 because its kinematics point to a birthplace in the metal-poor rim of the Galactic disc. Here we report the atmosphere of HD 271791 to indeed show a sub-solar iron abundance along with an enhancement of the alpha -elements, indicating capture of nucleosynthesis products from a supernova or a more energetic hypernova. This implies that HD 271791 is the surviving secondary of a massive binary system disrupted in a supernova explosion. No such run-away star has ever been found to exceed the Galactic escape velocity, hence HD 271791 is the first hyper-runaway star. Such a run-away scenario is an alternative to the Hills mechanism for the acceleration of some HVSs with moderate velocities. The observed chemical composition of HD 271791 puts invaluable observational constraints on nucleosynthesis in a supernova from the core-collapse of a very massive star (M_ZAMS > 55 M_o), which may be observed as a gamma-ray burst of the long-duration/soft-spectrum type.