  We report the results of an almost complete survey of the X-ray properties of
Hickson's compact galaxy groups with the ROSAT PSPC. Diffuse X-ray emission is
detected from 22 groups. We infer that hot intragroup gas is present in
$\gtsimm 75\%$ of these systems and derive their X-ray luminosity function.
Earlier reports that only spiral-poor systems exhibit diffuse X-ray emission
are found to be incorrect. Strong correlations are found between the X-ray
luminosity and both the gas temperature and the velocity dispersion of the
group galaxies. We argue that these properties provide strong evidence that
most of these groups are genuinely compact configurations, rather than
line-of-sight superpositions. Comparison with the X-ray properties of galaxy
clusters indicate a significant steepening of the $L:T$ relation below
$T\sim1$\keV, which may result from the action of galaxy winds.
