A critical early step in drug discovery is the screening of a chemical library. Typically, promising compounds are identified in a primary screen and then more fully characterized in a dose-response analysis with 7-10 data points per compound. Here, we describe a robust microfluidic approach that increases the number of data points to approximately 10,000 per compound. The system exploits Taylor-Aris dispersion to create concentration gradients, which are then segmented into picoliter microreactors by droplet-based microfluidics. The large number of data points results in IC(50) values that are highly precise (± 2.40% at 95% confidence) and highly reproducible (CV = 2.45%, n = 16). In addition, the high resolution of the data reveals complex dose-response relationships unambiguously. We used this system to screen a chemical library of 704 compounds against protein tyrosine phosphatase 1B, a diabetes, obesity, and cancer target. We identified a number of novel inhibitors, the most potent being sodium cefsulodine, which has an IC(50) of 27 ± 0.83 μM.