  We introduce a $\mathbb{Z}$-valued cross ratio on Roller boundaries of ${\rm
CAT(0)}$ cube complexes. We motivate its relevance by showing that every
cross-ratio preserving bijection of Roller boundaries uniquely extends to a
cubical isomorphism. Our results are strikingly general and even apply to
infinite dimensional, locally infinite cube complexes with trivial automorphism
group.
