Connectivity determines the function of neural circuits. Historically, circuit mapping has usually been viewed as a problem of microscopy, but no current method can achieve high-throughput mapping of entire circuits with single neuron precision. Here we describe a novel approach to determining connectivity. We propose BOINC ("barcoding of individual neuronal connections"), a method for converting the problem of connectivity into a form that can be read out by high-throughput DNA sequencing. The appeal of using sequencing is that its scale--sequencing billions of nucleotides per day is now routine--is a natural match to the complexity of neural circuits. An inexpensive high-throughput technique for establishing circuit connectivity at single neuron resolution could transform neuroscience research.