  A set of stacked two-dimensional electron systems in a perpendicular magnetic
field exhibits a three-dimensional version of the quantum Hall effect if
interlayer tunneling is not too strong. When such a sample is in a quantum Hall
plateau, the edge states of each layer combine to form a chiral metal at the
sample surface. We study the interplay of interactions and disorder in
transport properties of the chiral metal, in the regime of weak interlayer
tunneling. Our starting point is a system without interlayer tunneling, in
which the only excitations are harmonic collective modes: surface
magnetoplasmons. Using bosonization and working perturbatively in the
interlayer tunneling amplitude, we express transport properties in terms of the
spectrum for these collective modes, treating electron-electron interactions
and impurity scattering exactly. We calculte the conductivity as a function of
temperature, finding that it increases with increasing temperature as observed
in recent experiments. We also calculate the autocorrelation function of
mesoscopic conductance fluctuations induced by changes in a magnetic field
component perpendicular to the sample surface, and its dependence on
temperature. We show that conductance fluctuations are characterised by a
dephasing length that varies inversely with temperature.
