We predict a new effect in electronic bilayers: spin Hall drag. The effect consists of 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, while generally quite small, should be observable in optical rotation experiments.