The Seyfert 1 galaxy 1H 0419-577 hosts a ∼kpc extended outflow that is evident in the [O iii] image and that is also detected as a warm absorber in the UV/X-ray spectrum. Here, we analyze a ∼30 ks Chandra-ACIS X-ray image, with the aim of resolving the diffuse extranuclear X-ray emission and of investigating its relationship with the galactic outflow. Thanks to its sub-arcsecond spatial resolution, Chandra resolves the circumnuclear X-ray emission, which extends up to a projected distance of at least ∼16 kpc from the center. The morphology of the diffuse X-ray emission is spherically symmetrical. We could not recover a morphological resemblance between the soft X-ray emission and the ionization bicone that is traced by the [O iii] outflow. Our spectral analysis indicates that one of the possible explanations for the extended emission is thermal emission from a low-density (n H ∼ 10 −3 cm −3 ) hot plasma (T e ∼ 0.22 keV). If this is the case, we may be witnessing the cooling of a shock-heated wind bubble. In this scenario, the [O iii] emission line and the X-ray/UV absorption lines may trace cooler clumps that are entrained in the hot outflow. Alternatively, the extended emission could be to due to a blend of emission lines from a photoionized gas component having a hydrogen column density of N H ∼ 2.1×10 22 cm −2 and an ionization parameter of log ξ ∼ 1.3. Because the source is viewed almost edge-on we argue that the photoionized gas nebula must be distributed mostly along the polar directions, outside our line of sight. In this geometry, the X-ray/UV warm absorber must trace a different gas component, physically disconnected from the emitting gas, and located closer to the equatorial plane.