A theory is presented for the movement of a vesicle in response to a gradient in concentration of an impermeable molecular solute. The vesicle is a fluid sphere bounded by a rigid semipermeable membrane which prevents solute from crossing it. The external solute gradient acts as an osmotic driving force for solvent exchange across the membrane; thus, the membrane converts the solute gradient into mechanical stresses which propel the vesicle toward regions of lower solute concentration. The speed of the vesicle is essentially independent of the fluid viscosity, only weakly dependent on the vesicle size, and directly proportional to the solute concentration gradient in the external fluid.