In many situations, such as pedestrians crossing a busy street or prey evading predators, rapid decisions based on limited perceptual information are critical for survival. The brevity of these perceptual judgments constrains how neuronal signals are integrated or pooled over time because the underlying sequence of processes, from sensation to perceptual evaluation to motor planning and execution, all occur within several hundred milliseconds. Because most previous physiological studies of these processes have relied on tasks requiring considerably longer temporal integration, the neuronal basis of such rapid decisions remains largely unexplored. In this study, we examine the temporal precision of neuronal activity associated with a rapid perceptual judgment. We find that the activity of individual neurons over tens of milliseconds can reliably convey information about sensory events and was well correlated with the animals' judgments. There was a strong correlation between sensory reliability and the correlation with behavioral choice, suggesting that rapid decisions were preferentially based on the most reliable sensory signals. We also find that, a simple model in which the responses of individual neurons are summed is unable to explain behavioral performance. These results suggest that neuronal circuits are sufficiently precise to allow for cognitive decisions to be based on small numbers of action potentials from highly reliable neurons.