We present interstellar gas-phase abundances of zinc and chromium in the Milky Way for comparison with the abundances of these elements in damped Ly alpha systems at redshifts near z similar to 2. We make use of both IUE and GHRS archival information in deriving the Milky Way values and find that the average difference in [Zn/H] and [Cr/Zn] between the Milky Way and damped Ly alpha systems at large N(H I) is about 0.9 dex. The Zn/H values we find for the Milky Way are approximate to -0.2 to -0.7 dex below solar and are due in large part to the depletion of Zn onto dust grains. The amount of this gas-phase depletion is variable and depends upon the H I column density and molecular fraction of the gas. Milky Way sight lines having low molecular fractions have values of [Zn/H] within approximate to 0.2 dex of the solar value. Combined with the larger values of [Cr/Zn] found for the damped Ly alpha systems, this result confirms that measures of [Zn/H] should accurately reflect the lower gas-phase abundances of Zn found in these systems.