We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation $n$ and the distribution of the displacements of its children depend on an environment indexed by the time $n$. The environment is supposed to be stationary and ergodic. For $A\subset \mathbb{R}$ , let $Z_n(A)$ be the number of particles of generation $n$ located in $A$. We show central limit theorems for the counting measure $Z_n(\cdot)$ with appropriate normalization.
