  The chemical abundances in damped Lyman-alpha systems (DLAs) show more than 2
orders of magnitude variation at a given epoch, possibly because DLAs arise in
a wide variety of host galaxies. This could significantly bias estimates of
chemical evolution. We explore the possibility that DLAs in which H_2
absorption is detected may trace cosmological chemical evolution more reliably
since they may comprise a narrower set of physical conditions. The 9 known H_2
absorption systems support this hypothesis: metallicity exhibits a faster, more
well-defined evolution with redshift than in the general DLA population. The
dust-depletion factor and, particularly, H_2 molecular fraction also show rapid
increases with decreasing redshift. We comment on possible observational
selection effects which may bias this evolution. Larger samples of H_2-bearing
DLAs are clearly required and may constrain evolution of the UV background and
DLA galaxy host type with redshift.
