  We present the deepest Chandra observation to date of the galaxy M84 in the
Virgo Cluster, with over 840 kiloseconds of data provided by legacy
observations and a recent 730 kilosecond campaign. The increased
signal-to-noise allows us to study the origins of the accretion flow feeding
the supermassive black hole in the center of M84 from the kiloparsec scales of
the X-ray halo to the Bondi radius, $R_{\rm B}$. Temperature, metallicity, and
deprojected density profiles are obtained in four sectors about M84's AGN,
extending into the Bondi radius. Rather than being dictated by the potential of
the black hole, the accretion flow is strongly influenced by the AGN's bipolar
radio jets. Along the jet axis, the density profile is consistent with $n_e
\propto r^{-1}$; however, the profiles flatten perpendicular to the jet. Radio
jets produce a significant asymmetry in the flow, violating a key assumption of
Bondi accretion. Temperature in the inner kiloparsec is approximately constant,
with only a slight increase from 0.6 to 0.7 keV approaching $R_{\rm B}$, and
there is no evidence for a temperature rise imposed by the black hole. The
Bondi accretion rate $\dot{M}_{\rm B}$ exceeds the rate inferred from AGN
luminosity and jet power by over four orders of magnitude. In sectors
perpendicular to the jet, $\dot{M}_{\rm B}$ measurements agree; however, the
accretion rate is $> 4 \sigma$ lower in the North sector along the jet, likely
due to cavities in the X-ray gas. Our measurements provide unique insight into
the fueling of AGN responsible for radio mode feedback in galaxy clusters.
