  We consider the maximum $M_t$ of branching random walk in a
space-inhomogeneous random environment on $\mathbb{Z}$. In this model the
branching rate while at some location $x\in\mathbb{Z}$ is randomized in an
i.i.d.\@ manner. We prove that there is a centering $\widetilde{m}_t$ depending
only on the environment such that $(M_t-\widetilde{m}_t)_{t\ge 0}$ is tight in
an annealed sense.
