  For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a
compact manifold with boundary $(M^{n+1},\partial M)$, $3\leq (n + 1)\leq 7$,
we prove that, for any open subset $V$ of $\partial M$, there exists a compact,
properly embedded free boundary minimal hypersurface intersecting $V$.
