  Let $G$ be a semisimple Lie group without compact factor and $\Gamma < G$ a
torsion-free, cocompact, irreducible lattice. According to Selberg, periodic
orbits of regular Weyl chamber flows live on maximal flat periodic tori of the
space of Weyl chambers. We prove that these flat periodic tori equidistribute
exponentially fast towards the quotient of the Haar measure. From the
equidistribution formula, we deduce a higher rank prime geodesic theorem. These
counting and equidistribution results also hold in the non cocompact, finite
covolume case for $G=\mathrm{SL}(d,\mathbb{R})$ and
$\Gamma<\mathrm{SL}(d,\mathbb{Z})$ a finite index subgroup.
