Various techniques designed to extract nonlinear characteristics from experimental time series have provided no clear evidence as to whether the electroencephalogram (EEG) is chaotic. Compounding the lack of firm experimental evidence is the paucity of physiologically plausible theories of EEG that are capable of supporting nonlinear and chaotic dynamics. Here we provide evidence for the existence of chaotic dynamics in a neurophysiologically plausible continuum theory of electrocortical activity and show that the set of parameter values supporting chaos within parameter space has positive measure and exhibits fat fractal scaling.