  We present a Chandra observation of the only low redshift, z=0.299, galaxy
cluster to contain a highly luminous radio-quiet quasar, H1821+643. By
simulating the quasar PSF, we subtract the quasar contribution from the cluster
core and determine the physical properties of the cluster gas down to 3 arcsec
(15 kpc) from the point source. The temperature of the cluster gas decreases
from 9.0\pm0.5 keV down to 1.3\pm0.2 keV in the centre, with a short central
radiative cooling time of 1.0\pm0.1 Gyr, typical of a strong cool-core cluster.
The X-ray morphology in the central 100 kpc shows extended spurs of emission
from the core, a small radio cavity and a weak shock or cold front forming a
semi-circular edge at 15 arcsec radius. The quasar bolometric luminosity was
estimated to be 2 x 10^{47} erg per sec, requiring a mass accretion rate of 40
Msolar per yr, which corresponds to half the Eddington accretion rate. We
explore possible accretion mechanisms for this object and determine that Bondi
accretion, when boosted by Compton cooling of the accretion material, could
provide a significant source of the fuel for this outburst. We consider
H1821+643 in the context of a unified AGN accretion model and, by comparing
H1821+643 with a sample of galaxy clusters, we show that the quasar has not
significantly affected the large-scale cluster gas properties.
