Decisions about the visual world can take time to form, especially when information is unreliable. We studied the neural correlate of gradual decision formation by recording activity from the lateral intraparietal cortex (area LIP) of rhesus monkeys during a combined motion-discrimination reaction-time task. Monkeys reported the direction of random-dot motion by making an eye movement to one of two peripheral choice targets, one of which was within the response field of the neuron. We varied the difficulty of the task and measured both the accuracy of direction discrimination and the time required to reach a decision. Both the accuracy and speed of decisions increased as a function of motion strength. During the period of decision formation, the epoch between onset of visual motion and the initiation of the eye movement response, LIP neurons underwent ramp-like changes in their discharge rate that predicted the monkey's decision. A steeper rise in spike rate was associated with stronger stimulus motion and shorter reaction times. The observations suggest that neurons in LIP integrate time-varying signals that originate in the extrastriate visual cortex, accumulating evidence for or against a specific behavioral response. A threshold level of LIP activity appears to mark the completion of the decision process and to govern the tradeoff between accuracy and speed of perception.