  We calculate the quasiparticle contribution to the zero temperature Hall
conductance of two-dimensional extreme type-II superconductors in a high
magnetic field, using the Landau basis. As one enters the superconducting phase
the Hall conductance is renormalized to smaller values, with respect to the
normal state result, until a quantum level-crossing transition is reached. At
high values of the order parameter, where the quasiparticles are bound to the
vortex cores, the Hall conductance is expected to tend to zero due to a theorem
of Thouless.
