  Let $\Gamma$ be a torsion-free lattice of $\text{PU}(p,1)$ with $p \geq 2$
and let $(X,\mu_X)$ be an ergodic standard Borel probability $\Gamma$-space. We
prove that any maximal Zariski dense measurable cocycle $\sigma: \Gamma \times
X \longrightarrow \text{SU}(m,n)$ is cohomologous to a cocycle associated to a
representation of $\text{PU}(p,1)$ into $\text{SU}(m,n)$, with $1 < m \leq n$.
The proof follows the line of Zimmer' Superrigidity Theorem and requires the
existence of a boundary map, that we prove in a much more general setting. As a
consequence of our result, it cannot exist a maximal measurable cocycle with
the above properties when $n\neq m$.
