Response time (RT) is a commonly used measure of cognitive performance, which is usually characterized as stochastic. However, useful information may be hidden in the apparently random fluctuations of RT. Dynamical systems analysis techniques allow an exploration of the alternative hypothesis that RT fluctuations are deterministic, albeit in a complex manner. We applied careful task construction and noise-reduction and surrogate series tests to show that RT series from a forced-pace serial response-time task have low-dimensional chaotic characteristics. In Experiment 1, 80% of subjects' filtered RT series had low dimensionality, sensitive dependence on initial conditions, spectra close to 1/f, and stable attractor geometry across sessions. In Experiment 2, we showed that the size of the inter-stimulus interval (ISI) determined the number of subjects with low-dimensional chaotic series. A small ISI caused 100% of subjects to respond in the chaotic regime, whereas only 25% had a low-dimensional chaotic RT component when the ISI was large. We argue that demanding task requirements cause a reduction in the dimensionality of the dynamics, producing RT fluctuations that may reflect a response strategy for controlling RT.