Computer control of Darwinian evolution has been demonstrated by propagating a population of RNA enzymes in a microfluidic device. The RNA population was challenged to catalyze the ligation of an oligonucleotide substrate under conditions of progressively lower substrate concentrations. A microchip-based serial dilution circuit automated an exponential growth phase followed by a 10-fold dilution, which was repeated for 500 log-growth iterations. Evolution was observed in real time as the population adapted and achieved progressively faster growth rates over time. The final evolved enzyme contained a set of 11 mutations that conferred a 90-fold improvement in substrate utilization, coinciding with the applied selective pressure. This system reduces evolution to a microfluidic algorithm, allowing the experimenter to observe and manipulate adaptation.