We report the discovery of a dwarf (MB = -13.9) poststarburst galaxy coincident in recession velocity (within uncertainties) with the highest column density absorber (NHI = 1015.85 cm-2 at cz = 1586 km s-1) in the 3C 273 sight line. This galaxy is by far the closest galaxy to this absorber, projected just 71 h70-1 kpc on the sky from the sight line. The mean properties of the stellar populations in this galaxy are consistent with a massive starburst ≈3.5 Gyr ago, whose attendant supernovae, we argue, could have driven sufficient gas from this galaxy to explain the nearby absorber. Beyond its proximity on the sky and in recession velocity, the further evidence in favor of this conclusion includes both a match in the metallicities of absorber and galaxy and the fact that the absorber has an overabundance of Si/C, suggesting recent Type II supernova enrichment. Thus, this galaxy and its ejecta are in the expected intermediate stage in the fading dwarf evolutionary sequence envisioned by Babul & Rees to explain the abundance of faint blue galaxies at intermediate redshifts. While this one instance of a QSO metal-line absorber and a nearby dwarf galaxy is not proof of a trend, a similar dwarf galaxy would be too faint to be observed by galaxy surveys around more distant metal-line absorbers. Thus, we cannot exclude the possibility that dwarf galaxies are primarily responsible for weak (NHI = 1014-1017 cm-2) metal-line absorption systems in general. If a large fraction of the dwarf galaxies expected to exist at high redshift had a similar history (i.e., they had a massive starburst that removed all or most of their gas), these galaxies could account for at least several hundred high-z metal-line absorbers along the line of sight to a high-z QSO. The volume-filling factor for this gas, however, would be less than 1%.