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.