The anatomical connectivity of the nervous system of the nematode Caenorhabditis elegans has been almost completely described, but determination of the neurophysiological basis of behavior in this system is just beginning. Here we used an optimization algorithm to search for patterns of connectivity sufficient to compute the sensorimotor transformation underlying C. elegans chemotaxis, a simple form of spatial orientation behavior in which turning probability is modulated by the rate of change of chemical concentration. Optimization produced differentiator networks capable of simulating chemotaxis. A surprising feature of these networks was inhibitory feedback connections on all neurons. Further analysis showed that feedback regulates the latency between sensory input and behavior. Common patterns of connectivity between the model and biological networks suggest new functions for previously identified connections in the C. elegans nervous system.