  The formation of globular clusters and their relation to the distribution of
dark matter have long puzzled astronomers. One of the most recently-proposed
globular cluster formation channels ties ancient star clusters to the
large-scale streaming velocity of baryons relative to dark matter in the early
Universe. These streaming velocities affect the global infall of baryons into
dark matter halos, the high-redshift halo mass function, and the earliest
generations of stars. In some cases, streaming velocities may result in dense
regions of dark-matter-free gas that becomes Jeans unstable, potentially
leading to the formation of compact star clusters. We investigate this
hypothesis using cosmological hydrodynamical simulations that include a full
chemical network and the formation and destruction of H$_2$, a process crucial
for the formation of the first stars. We find that high-density gas in regions
with significant streaming velocities -- which constitute approximately 1\% of
the Universe -- is indeed somewhat offset from the centers of dark matter
halos, but this offset is typically significantly smaller than the virial
radius. Gas outside of dark matter halos never reaches Jeans-unstable densities
in our simulations. We postulate that low-level ($Z \approx
10^{-3}\,Z_{\odot}$) metal enrichment by Population III supernovae may enable
cooling in the extra-virial regions, allowing gas outside of dark matter halos
to cool to the CMB temperature and become Jeans-unstable. Follow-up simulations
that include both streaming velocities and metal enrichment by Population III
supernovae are needed to understand if streaming velocities provide one path
for the formation of globular clusters in the early Universe.
