  In this paper we demonstrate the possibility of dissipationless spin
transport in the chiral d-density wave state, by the sole application of a
uniform Zeeman field gradient. The occurrence of these spontaneous spin
currents is attributed to the parity (${\cal P}$) and time-reversal (${\cal
T}$) violation induced by the $d_{xy}+id_{x^2-y^2}$ density wave order
parameter. We calculate the spin Hall conductance and reveal its intimate
relation to the Berry phase which is generated when the Zeeman field is applied
adiabatically. Finally, we demonstrate that in the zero temperature and doping
case, the spin Hall conductance is quantized as it becomes a topological
invariant.
