  Recent analysis of five gamma-ray burst (GRB) afterglow spectra reveal the
absence of molecular hydrogen absorption lines, a surprising result in light of
their large neutral hydrogen column densities and the detection of H$_2$ in
similar, more local star-forming regions like 30 Doradus in the Large
Magellanic Cloud (LMC). Observational evidence further indicates that the bulk
of the neutral hydrogen column in these sight lines lies 100 pc beyond the
progenitor and that H$_2$ was absent prior to the burst, suggesting that direct
flux from the star, FUV background fields, or both suppressed its formation. We
present one-dimensional radiation hydrodynamical models of GRB host galaxy
environments, including self-consistent radiative transfer of both ionizing and
Lyman-Werner photons, nine-species primordial chemistry with dust formation of
H$_2$, and dust extinction of UV photons. We find that a single GRB progenitor
is sufficient to ionize neutral hydrogen to distances of 50 - 100 pc but that a
galactic Lyman-Werner background is required to dissociate the molecular
hydrogen in the ambient ISM. Intensities of 0.1 - 100 times the Galactic mean
are necessary to destroy H$_2$ in the cloud, depending on its density and
metallicity. The minimum radii at which neutral hydrogen will be found in
afterglow spectra is insensitive to the mass of the progenitor or the initial
mass function (IMF) of its cluster, if present.
