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

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... re Weyl fermions connected by surface Fermi arcs. We show that the 3D anomalous Hall conductivity is e^2/(√(3)ah), with a the lattice constant.