Deep γ-ray observations of the Galactic Centre with arcminute angular resolution show traces of petaelectronvolt protons within the central ten parsecs of our Galaxy; the accelerator of these particles could have provided a substantial contribution to Galactic cosmic rays in the past. This paper from the HESS (High Energy Stereoscopic System) Collaboration presents deep γ-ray observations with arcminute angular resolution of the Galactic Centre regions, which show the tracer of the presence of particles accelerated to energies of at least a few petaelectronvolts (1 PeV = 1015 electronvolts) within the central 10 parsecs of our Galaxy. This is consistent with previous observations of PeV Galactic cosmic rays and requires the presence of a source capable of accelerating particles to such extreme energies. The authors argue that the source is the supermassive black hole Sagittarius A*. Although the current rate of particle acceleration due to Sagittarius A* is not sufficient to provide a substantial contribution to Galactic cosmic rays, it could have plausibly been more active in the past. Galactic cosmic rays reach energies of at least a few petaelectronvolts1 (of the order of 1015 electronvolts). This implies that our Galaxy contains petaelectronvolt accelerators (‘PeVatrons’), but all proposed models of Galactic cosmic-ray accelerators encounter difficulties at exactly these energies2. Dozens of Galactic accelerators capable of accelerating particles to energies of tens of teraelectronvolts (of the order of 1013 electronvolts) were inferred from recent γ-ray observations3. However, none of the currently known accelerators—not even the handful of shell-type supernova remnants commonly believed to supply most Galactic cosmic rays—has shown the characteristic tracers of petaelectronvolt particles, namely, power-law spectra of γ-rays extending without a cut-off or a spectral break to tens of teraelectronvolts4. Here we report deep γ-ray observations with arcminute angular resolution of the region surrounding the Galactic Centre, which show the expected tracer of the presence of petaelectronvolt protons within the central 10 parsecs of the Galaxy. We propose 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 outbursts5and an outflow from the Galactic Centre6. 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 106–107 years, and therefore should be considered as a viable alternative to supernova remnants as a source of petaelectronvolt Galactic cosmic rays.