  We show that an almost Hermitian manifold $(M,g)$ of real dimension $4n$
which is strongly asymptotic to $\mathbb{C}H^{2n}$ and satisfies a certain
scalar curvature bound must be isometric to the complex hyperbolic space.
Assuming K\"ahler instead of almost Hermitian this gives the already known
rigidity result by H. Boualem and M. Herlich proved in \emph{Ann. Scuola Norm.
Sup Pisa (Ser. V)}, vol. 1(2).
