  We prove the following result that was conjectured by Brunella: Let $X$ be a
compact complex manifold of dimension $\geq 3$. Let $\mathcal{F}$ be a
codimension one holomorphic foliation on $X$ with ample normal bundle. Then
every leaf of $\mathcal{F}$ accumulates to the singular set of $\mathcal{F}$.
