  Let $B =\{ B_t \, : \, t \geq 0 \}$ be a real-valued fractional Brownian
motion of index $H \in (0,1)$. We prove that the macroscopic Hausdorff
dimension of the level sets $\mathcal{L}_x = \left\{ t \in \mathbb{R}_+ \, : \,
B_t=x \right\}$ is, with probability one, equal to $1-H$ for all
$x\in\mathbb{R}$.
