  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.
