  We consider the Hall effect in a system of weakly coupled Luttinger chains.
We obtain the full conductivity tensor in the absence of dissipation along the
chains. We show that while the dependence of the Hall and transverse
conductivities on temperature and frequency are affected by the Luttinger
interaction very strongly, the Hall resistivity is given by a simple formula
corresponding to the noninteracting fermions. We compute the frequency,
temperature and field dependence of the transverse conductivity. Consequences
for the quasi-one-dimensional organic conductors are discussed.
