We study the cool gas around a galaxy at z = 0.4729 using Keck/LRIS spectroscopy of a bright (B = 21.7) background galaxy at z = 0.6942 at a transverse distance of 16.5/h_70 kpc. The background galaxy spectrum reveals strong FeII, MgII, MgI, and CaII absorption at the redshift of the foreground galaxy, with a MgII 2796 rest equivalent width of 3.93 +/- 0.08 Angstroms, indicative of a velocity width exceeding 400 km/s. Because the background galaxy is large (> 4/h_70 kpc), the high covering fraction of the absorbing gas suggests that it arises in a spatially extended complex of cool clouds with large velocity dispersion. Spectroscopy of the massive (log M_*/M_sun = 11.15 +/- 0.08) host galaxy reveals that it experienced a burst of star formation about 1 Gyr ago and that it harbors a weak AGN. We discuss the possible origins of the cool gas in its halo, including multiphase cooling of hot halo gas, cold inflow, tidal interactions, and galactic winds. We conclude the absorbing gas was most likely ejected or tidally stripped from the interstellar medium of the host galaxy or its progenitors during the past starburst event. Adopting the latter interpretation, these results place one of only a few constraints on the radial extent of cool gas driven or stripped from a galaxy in the distant Universe. Future studies with integral field unit spectroscopy of spatially extended background galaxies will provide multiple sightlines through foreground absorbers and permit analysis of the morphology and kinematics of the gas surrounding galaxies with a diverse set of properties and environments.
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