  We address the role of short range interactions for spinless fermions in the
hyperhoneycomb lattice, a three dimensional (3D) structure where all sites have
a planar trigonal connectivity. For weak interactions, the system is a
line-node semimetal. In the presence of strong interactions, we show that the
system can be unstable to a 3D quantum anomalous Hall phase with loop currents
that break time reversal symmetry, as in the Haldane model. We find that the
low energy excitations of this state are Weyl fermions connected by surface
Fermi arcs. We show that the 3D anomalous Hall conductivity is
$e^{2}/(\sqrt{3}ah)$, with $a$ the lattice constant.
