  We study the chemical abundances of the interstellar medium surrounding high
z gamma-ray bursts (GRBs) through analysis of the damped Lya systems (DLAs)
identified in afterglow spectra. These GRB-DLAs are characterized by large HI
column densities N(HI) and metallicities [M/H] spanning 1/100 to nearly solar,
with median [M/H]>-1. The majority of GRB-DLAs have [M/H] values exceeding the
cosmic mean metallicity of atomic gas at z>2, i.e. if anything, the GRB-DLAs
are biased to larger metallicity. We also observe (i) large [Zn/Fe] values
(>+0.6) and sub-solar Ti/Fe ratios which imply substantial differential
depletion, (ii) large a/Fe ratios suggesting nucleosynthetic enrichment by
massive stars, and (iii) low C^0/C^+ ratios (<10^{-4}). Quantitatively, the
observed depletion levels and C^0/C^+ ratios of the gas are not characteristic
of cold, dense HI clouds in the Galactic ISM. We argue that the GRB-DLAs
represent the ISM near the GRB but not gas directly local to the GRB (e.g. its
molecular cloud or circumstellar material). We compare these observations with
DLAs intervening background quasars (QSO-DLAs). The GRB-DLAs exhibit larger
N(HI) values, higher a/Fe and Zn/Fe ratios, and have higher metallicity than
the QSO-DLAs. We argue that the differences primarily result from
galactocentric radius-dependent differences in the ISM: GRB-DLAs preferentially
probe denser, more depleted, higher metallicity gaslocated in the inner few kpc
whereas QSO-DLAs are more likely to intersect the less dense, less enriched,
outer regions of the galaxy. Finally, we investigate whether dust obscuration
may exclude GRB-DLA sightlines from QSO-DLA samples; we find that the majority
of GRB-DLAs would be recovered which implies little observational bias against
large N(HI) systems.
