There is evidence in 21cm HI emission for voids several kpc in size centered approximately on the Galactic centre, both above and below the Galactic plane. These appear to map the boundaries of the Galactic nuclear wind. An analysis of HI at the tangent points, where the distance to the gas can be estimated with reasonable accuracy, shows a sharp transition at Galactic radii $Rlesssim 2.4$ kpc from the extended neutral gas layer characteristic of much of the Galactic disk, to a thin Gaussian layer with FWHM $sim 125$ pc. An anti-correlation between HI and $gamma$-ray emission at latitudes $10^{circ} leq |b| leq 20^{circ}$ suggests that the boundary of the extended HI layer marks the walls of the Fermi Bubbles. With HI we are able to trace the edges of the voids from $|z| > 2$ kpc down to $zapprox0$, where they have a radius $sim 2$ kpc. The extended HI layer likely results from star formation in the disk, which is limited largely to $R gtrsim 3$ kpc, so the wind may be expanding into an area of relatively little HI. Because the HI kinematics can discriminate between gas in the Galactic center and foreground material, 21cm HI emission may be the best probe of the extent of the nuclear wind near the Galactic plane.