  We analyzed a deep Chandra observation of M84, a bright elliptical galaxy in
the core of the Virgo cluster. We find that the spatial distribution of the
soft X-ray emission is defined by the radio structure of the galaxy. In
particular we find two low density regions associated with the radio lobes and
surrounded by higher density X-ray filaments. In addition to a central AGN and
a population of galactic sources, we find a diffuse hard source filling the
central 10 kpc region. Since the morphology of the hard source appears round
and is different from that seen in the radio or in soft X-rays, we propose that
it is hot gas heated by the central AGN. Finally, we find that the central
elemental abundance in the X-ray gas is comparable to that measured optically.
