  Let $M^n$ be a compact K\"ahler manifold with bisectional curvature bounded
from below by $1$. If $diam(M) = \pi / \sqrt{2}$ and $vol(M)>
vol(\mathbb{C}\mathbb{P}^n)/ 2^n$, we prove that $M$ is biholomorphically
isometric to $\mathbb{C}\mathbb{P}^n$ with the standard Fubini-Study metric.
