Abstract: Like other spiral galaxies, the Milky Way drives a biconical nuclear wind. Outflowing gas is visible in enhanced emission in many parts of the electromagnetic spectrum, including Fermi gamma-ray bubbles and radio lobes extending above and below the Galactic Center. We present early results from a 49-orbit Hubble Space Telescope program to study the kinematics and extent of the nuclear outflow, using UV absorption-line spectroscopy of AGN and halo stars lying close on the sky to the Galactic Center. The variation in absorption properties with Galactic latitude allows us to constrain the physical conditions in the outflowing gas. We present the first constraint on the nuclear outflow velocity (~900-1000 km/s) using kinematic outflow modeling of the absorption components observed in the spectrum of the QSO PDS456, which lies behind the base of the Fermi Bubbles near the Galactic Center (l,b=10.4, +11.2 degrees).