We report an effective solution to the macroscopic/microfluidic interface issue and demonstrate how microfluidics can achieve impressive economies of scale in reducing the complexity of pipetting operations. Using an N x N microfluidic matrix with N = 20, we performed N2 = 400 distinct PCR reactions with only 2N + 1 = 41 pipetting steps, compared with the 3N2 = 1200 steps required with conventional fluid handling. Each vertex of the matrix has a 3-nL reactor, and a single 2-microL aliquot of polymerase is amortized over all 400 independent reactions, thus dramatically reducing sample overhead and minimizing reagent consumption. Beyond PCR, the matrix chip provides a general method to perform chemical and biological experiments with precious reagents in a highly automated fashion.