  We report the Chandra detection of X-ray emission spatially coincident with
the kpc-scale radio bubbles in the nearby (D_L ~ 31 Mpc) AGN-starburst galaxy
NGC 6764. The X-ray emission originates in hot gas (kT ~ 0.75 keV), which may
either be contained within the radio bubbles, or in a shell of hot gas
surrounding them. We consider three models for the origin of the hot gas: (1) a
starburst-driven galactic wind, (2) shocked gas associated with the expanding
radio bubbles, and (3) gas heated and entrained into the bubbles by jet/ISM
interactions in the inner AGN outflow. We rule out a galactic wind based on
significant differences from known galactic wind systems. The tight
correspondence between the brightest X-ray emission and the radio emission in
the inner outflow from the Seyfert nucleus, as well as a correlation between
X-ray and radio spectral features suggestive of shocks and particle
acceleration, lead us to favour the third model; however, we cannot firmly rule
out a model in which the bubbles are driving large-scale shocks into the galaxy
ISM. In either AGN-driven heating scenario, the total energy stored in the hot
gas is high, ~10^56 ergs, comparable to the energetic impact of low-power radio
galaxies such as Centaurus A, and will have a dramatic impact on the galaxy and
its surroundings.

Astrophysics