  We explore the clustering properties of high redshift dark matter halos,
focusing on halos massive enough to host early generations of stars or galaxies
at redshift 10 and greater. Halos are extracted from an array of dark matter
simulations able to resolve down to the "mini-halo" mass scale at redshifts as
high as 30, thus encompassing the expected full mass range of halos capable of
hosting luminous objects and sources of reionization. Halo clustering on
large-scales agrees with the Sheth, Mo & Tormen halo bias relation within all
our simulations, greatly extending the regime where large-scale clustering is
confirmed to be "universal" at the 10-20% level (which means, for example, that
3sigma halos of cluster mass at z=0 have the same large-scale bias with respect
to the mass distribution as 3sigma halos of galaxy mass at z=10). However, on
small-scales, the clustering of our massive halos (> ~10^9 Msun/h) at these
high redshifts is stronger than expected from comparisons with small-scale halo
clustering extrapolated from lower redshifts. This implies "non-universality"
in the scale-dependence of halo clustering, at least for the commonly used
parameterizations of the scale-dependence of bias that we consider. We provide
a fit for the scale-dependence of bias in our results. This study provides a
basis for using extraordinarily high redshift galaxies (redshift ~10) as a
probe of cosmology and galaxy formation at its earliest stages. We show also
that mass and halo kinematics are strongly affected by finite simulation
volumes. This suggests the potential for adverse affects on gas dynamics in
hydrodynamic simulations of limited volumes, such as is typical in simulations
of the formation of the "first stars", though further study is warranted.
