This paper demonstrates a microfluidic system that automates i) formation of a lipid bilayer at the interface between a pair of nanoliter-sized aqueous droplets in oil, ii) exchange of one droplet of the pair to form a new bilayer, and iii) current measurements on single proteins. A new microfluidic architecture is introduced – a set of traps designed to localize the droplets with respect to each other and with respect to the recording electrodes. The system allows for automated execution of experimental protocols by active control of the flow on chip with the use of simple external valves. Formation of stable artificial lipid bilayers, incorporation of α-hemolysin into the bilayers and electrical measurements of ionic transport through the protein pore are demonstrated.