  We consider branching random walk in random environment (BRWRE) and prove the
existence of deterministic subsequences along which their maximum, centered at
its mean, is tight. This partially answers an open question in
arXiv:1711.00852. The method of proof adapts an argument developed by Dekking
and Host for branching random walks with bounded increments. The question of
tightness without the need for subsequences remains open.
