Galactic cosmic rays reach energies of at least a few Peta-electronvolts (1 PeV =1015 electron volts)1 . This implies our Galaxy contains PeV accelerators (PeVatrons), but all proposed models of Galactic cosmic-ray accelerators encounter non-trivial difficulties at exactly these energies 2 . Tens of Galactic accelerators capable of accelerating particle to tens of TeV (1 TeV =10 12 electron volts) energies were inferred from recent gamma-ray observations 3 . None of the currently known accelerators, however, not even the handful of shell-type supernova remnants commonly believed to supply most Galactic cosmic rays, have shown the characteristic tracers of PeV particles: power-law spectra of gamma rays extending without a cutoff or a spectral break to tens of TeV 4 . Here we report deep gamma-ray observations with arcminute angular resolution of the Galactic Centre regions, which show the expected tracer of the presence of PeV particles within the central 10 parsec of the Galaxy. We argue that the supermassive black hole Sagittarius A* is linked to this PeVatron. Sagittarius A* went through active phases in the past, as demonstrated by X-ray outbursts 5 and an outflow from the Galactic Center 6 . Although its current rate of particle acceleration is not sufficient to provide a substantial contribution to Galactic cosmic rays, Sagittarius A* could have plausibly been more active over the last 10 6−7 years, and therefore should be considered as a viable alternative to supernova remnants as a source of PeV Galactic cosmic rays.The large photon statistics accumulated over the last 10 years of observations with the High Energy Stereoscopic System (H.E.S.S.), together with improvements in the methods of data analysis, allow for a deep study of the properties of the diffuse very-high-energy (VHE; more than 100 GeV) emission of the central molecular zone. This region surrounding the Galactic Centre contains predominantly molecular gas and extends (in projection) out to r∼250 pc at positive galactic longitudes and r∼150 pc at negative longitudes. The map of the central molecular zone as seen in VHE γ-rays (Fig. 1) shows a strong (although not linear; see below) correlation between the brightness distribution of VHE γ-rays and the locations of massive gas-rich complexes. This points towards a hadronic origin of the diffuse emission 7 , where the γ-rays result from the interactions of relativistic protons with the ambient gas. The second important mechanism of production of VHE γ-rays 3 is the inverse Compton scattering of electrons. However, the severe radiative losses suffered by multi-TeV electrons in the Galactic Centre region prevent them from propagating over scales comparable to the size of the central molecular zone, thus disfavouring a leptonic origin of the γ-rays (see discussion in Methods and Extended Data Figures 1 and 2). The location and the particle injection rate history of the cosmic-ray accelerator(s), responsible for the relativistic protons, determine the spatial distribution of these cosmic rays which...