  Systems with strong spin-orbit coupling, which competes with other
interactions and energy scales, offer a fertile playground to explore new
correlated phases of matter. Weyl semimetals are an example where the
phenomenon leads to a low energy effective theory in terms of massless linearly
dispersing fermions in three dimensions. In the absence of interactions
chirality is a conserved quantum number, protecting the semi-metallic physics
against perturbations that are translationally invariant. In this letter we
show that the interplay between interaction and topology yields a novel chiral
excitonic insulator. The state is characterized by a complex vectorial order
parameter leading to a gapping out of the Weyl nodes. A striking feature is
that it is ferromagnetic, with the phase of the order parameter determining the
direction of the induced magnetic moment.
