  We theoretically study the electronic band structure and the Hall effect in
the negatively-curved three-dimensional (3D) graphene network in magnetic
fields. We found that special energy regions appear above and below the
zero-energy Landau level, where the 3D Hall conductivity is quantized even
though the spectrum is not fully gapped. The energy regions are dominated by
the chiral snake states traveling along the zero magnetic field contour on the
3D surface, and the quantization of the Hall conductivity crucially depends on
the topology of the contour. The exclusive energy region for the chiral states
is found to be a universal feature of 3D graphene systems.
