We have developed a microfluidic technology for the fabrication of compositionally asymmetric giant unilamellar vesicles (GUVs). The vesicles are assembled in two independent steps. In each step, a lipid monolayer is formed at a water-oil interface. The first monolayer is formed inside of a microfluidic device with a multiphase droplet flow configuration consisting of a continuous oil stream in which water droplets are formed. These droplets are dispensed into a vessel containing a layer of oil over a layer of water. The second lipid monolayer is formed by transferring the droplets through this second oil-water interface by centrifugation. By dissolving different lipid compositions in the different oil phases, the composition of each leaflet of the resulting lipid bilayer can be controlled. We have demonstrated membrane asymmetry by showing differential fluorescence quenching of labeled lipids in each leaflet and by demonstrating that asymmetric GUVs will bind an avidin-coated surface only when biotinylated lipids are targeted to the outer leaflet. In addition, we have demonstrated the successful asymmetric targeting of phosphatidylserine lipids to each leaflet, producing membranes with a biomimetic and physiologically relevant compositional asymmetry.