  We predict a new effect in electronic bilayers: the {\it Spin Hall Drag}. The
effect consists in the generation of spin accumulation across one layer by an
electric current along the other layer. It arises from the combined action of
spin-orbit and Coulomb interactions. Our theoretical analysis, based on the
Boltzmann equation formalism, identifies two main contributions to the spin
Hall drag resistivity: the side-jump contribution, which dominates at low
temperature, going as $T^2$, and the skew-scattering contribution, which is
proportional to $T^3$. The induced spin accumulation is large enough to be
detected in optical rotation experiments.
