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We present the deepest Chandra observation to date of the galaxy M84 in the Virgo Cluster, with over 840 ks of data provided by legacy observations and a recent 730 ks campaign. The increased signal-to-noise ratio allows us to study the origins of the accretion flow feeding the supermassive black hole in the centre of M84 from the kiloparsec scales of the X-ray halo to the Bondi radius, RB. Temperature, metallicity, and deprojected density profiles are obtained in four sectors about M84’s active galactic nucleus (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 ne ∝ 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 RB, 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 >4σ lower in the North sector along the jet, likely due to cavities in the X-ray gas. Our measurements provide unique insight into the fuelling of AGN responsible for radio mode feedback in galaxy clusters.