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

3D Quantum Anomalous Hall Effect in Hyperhoneycomb Lattices