  In this article, we consider a complete, non-compact almost Hermitian
manifold whose curvature is asymptotic to that of the complex hyperbolic plane.
Under natural geometric conditions, we show that such a manifold arises as the
interior of a compact almost complex manifold whose boundary is a strictly
pseudoconvex CR manifold. Moreover, the geometric structure of the boundary can
be recovered by analysing the expansion of the metric near infinity.
