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Limiting dilution PCR has become an increasingly useful technique for the detection and quantification of rare species in a population, but the limit of detection and accuracy of quantification are largely determined by the number of reactions that can be analyzed. Increased throughput may be achieved by reducing the reaction volume and increasing processivity. We have designed a high-throughput microfluidic chip that encapsulates PCR reagents in millions of picoliter droplets in a continuous oil flow. The oil stream conducts the droplets through alternating denaturation and annealing zones, resulting in rapid (55 second cycles) and efficient PCR amplification. Inclusion of fluorescent probes in the PCR reaction mix permits the amplification process to be monitored within individual droplets at specific locations within the microfluidic chip. We show that amplification of a 245 bp Adenovirus product can be detected and quantified in 35 minutes at starting template concentrations as low as one template molecule per 167 droplets (0.003 pg/μL). The frequencies of positive reactions over a range of template concentrations agree closely with the frequencies predicted by Poisson statistics, demonstrating both the accuracy and sensitivity of this platform for limiting dilution and digital PCR applications.