We have made experimental studies of low-temperature, high-magnetic fi
eld electronic transport in layered, three-dimensional semiconductor s
tructures. In fields that produce the integer quantum Hall effect for
transport parallel to the layers, we find deep minima in the vertical
conductance G(zz). Between these quantum Hall states, the size depende
nce of G(zz) indicates that vertical transport is through the bulk. Wi
thin quantum Hall states, we find that vertical transport is along the
surface of the sample, via a ''sheath'' of extended surface states. T
his surface sheath is a novel two-dimensional system that exhibits a m
etallic conductivity much less than e(2)/h.