We present a method for performing polymerase chain reaction (PCR) using isolated droplets flowing in an immiscible fluorinated solvent system. Thanks to an optimized control of interfacial properties, we could achieve in this capillary-based system reproducible amplification factors, without any detectable contamination between neighboring droplets. The system is readily amenable to further miniaturization and automation and serves as the first step toward a clinically viable, high-throughput, quantitative continuous flow PCR apparatus.