  Exploiting a fundamental characteristic of galaxy assembly in the
{\Lambda}CDM paradigm, the observed spatial biasing and kinematics of
metal-poor globular star clusters are used to constrain the local reionization
epoch around individual galaxies. Selecting three galaxies located in different
environments, the first attempt at constraining the environmental propagation
of reionization in the local Universe is carried out. The joint constraint from
the three galaxies (z_reion = 10.5^{+1.0}_{-0.9}) agrees remarkably well with
the latest WMAP constraint on z_reion for a simple instantaneous reionization
model. More importantly, the range of z_reion values found here are consistent
with the global range of z_reion estimates from other observations. We
furthermore find a 1.7{\sigma} indication that reionization completed in
low-density environments before the intergalactic medium in high-density
environments was reionized. This is consistent with certain theoretical models
that predict that reionization was globally prolonged in duration, with neutral
hydrogen pockets surviving in high-density environments, even after the
surrounding regions were reionized. More generally, this work provides a useful
constraint on the formation history of galaxy stellar halos.
