When humans respond to sensory stimulation, their reaction times tend to be long and variable relative to neural transduction and transmission times. The neural processes responsible for the duration and variability of reaction times are not understood. Single-cell recordings in a motor area of the cerebral cortex in behaving rhesus monkeys (Macaca mulatta) were used to evaluate two alternative mathematical models of the processes that underlie reaction times. Movements were initiated if and only if the neural activity reached a specific and constant threshold activation level. Stochastic variability in the rate at which neural activity grew toward that threshold resulted in the distribution of reaction times. This finding elucidates a specific link between motor behavior and activation of neurons in the cerebral cortex.