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We study metal abundances in the z=0.9313 damped Lyα system observed along the two lines of sight, A and B, toward the gravitationally lensed double QSO HE 0512-3329. Spatially resolved Space Telescope Imaging Spectrograph spectra constrain the neutral-gas column density to be N(HI)=10^20.5/cm2 in both A and B. UV-visual Echelle Spectrograph spectra (spectral resolution FWHM=9.8 km/s) show, in contrast, significant line-of-sight differences in the column densities of Mn II and Fe II; these are not due to observational systematics. We find that [Mn/H]=-1.44 and [Fe/H]=-1.52 in damped Lyα system A, while [Mn/H]=-0.98 and [Fe/H]>-1.32, and possibly as high as [Fe/H]~-1, in damped Lyα system B. A careful assessment of possible systematic errors leads us to conclude that these transverse differences are significant at a 5 σ level or greater. Although nucleosynthesis effects may also be at play, we favor differential dust depletion as the main mechanism producing the observed abundance gradient. The transverse separation is 5 h^–1₇₀kpc at the redshift of the absorber, which is also likely to be the lensing galaxy. The derived abundances therefore probe two opposite sides of a single galaxy hosting both damped Lyα systems. This is the first time firm abundance constraints have been obtained for a single damped system probed by two lines of sight. The significance of this finding for the cosmic evolution of metals is discussed.