  Surface electron currents are studied for the integer quantum Hall effect in
three dimensions(3D) proposed previously by Kohmoto et al. and by Koshino et
al. We predict the current wraps the facets of the sample with its intensity
and direction dictated by 3D Chern numbers which are just the quantized Hall
conductivities in 3D ($\sigma_{xy}, \sigma_{zx}$), so a natural connection
exists between the surface and bulk currents just as in 2D. An experiment to
detect the 3D integer quantum Hall effect through the wrapping current is
proposed.
