The neural basis of time perception is unknown. Here we show that neurons in the posterior parietal cortex (area LIP) represent elapsed time relative to a remembered duration. We trained rhesus monkeys to report whether the duration of a test light was longer or shorter than a remembered "standard" (316 or 800 ms) by making an eye movement to one of two choice targets. While timing the test light, the responses of LIP neurons signaled changes in the monkey's perception of elapsed time. The variability of the neural responses explained the monkey's uncertainty about its temporal judgments. Thus, in addition to their role in spatial processing and sensorimotor integration, posterior parietal neurons encode signals related to the perception of time.