  Galactic cosmic rays reach energies of at least a few Peta-electronvolts (1
PeV =$10^\mathbf{15}$ electron volts). 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. Tens
of Galactic accelerators capable of accelerating particle to tens of TeV (1 TeV
=$10^\mathbf{12}$ electron volts) energies were inferred from recent gamma-ray
observations. 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. 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 and an outflow from the Galactic Centre.
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 $\gtrsim 10^{6-7}$ years, and
therefore should be considered as a viable alternative to supernova remnants as
a source of PeV Galactic cosmic rays.
