Evidence has mounted in recent decades that outflows of matter and energy from the central few parsecs of our Galaxy have shaped the observed structure of the Milky Way on a variety of larger scales1. On scales of 15 parsecs, the Galactic Centre has bipolar lobes that can be seen in both the X-ray and radio parts of the spectrum2,3, indicating broadly collimated outflows from the centre, directed perpendicular to the Galactic plane. On larger scales, approaching the size of the Galaxy itself, γ-ray observations have revealed the so-called ‘Fermi bubble’ features4, implying that our Galactic Centre has had a period of active energy release leading to the production of relativistic particles that now populate huge cavities on both sides of the Galactic plane. The X-ray maps from the ROSAT all-sky survey show that the edges of these cavities close to the Galactic plane are bright in X-rays4,5,6. At intermediate scales (about 150 parsecs), radio astronomers have observed the Galactic Centre lobe, an apparent bubble of emission seen only at positive Galactic latitudes7,8, but again indicative of energy injection from near the Galactic Centre. Here we report prominent X-ray structures on these intermediate scales (hundreds of parsecs) above and below the plane, which appear to connect the Galactic Centre region to the Fermi bubbles. We propose that these structures, which we term the Galactic Centre ‘chimneys’, constitute exhaust channels through which energy and mass, injected by a quasi-continuous train of episodic events at the Galactic Centre, are transported from the central few parsecs to the base of the Fermi bubbles4.