Human electroencephalogram (EEG) consists of complex aperiodic oscillations that are assumed to indicate underlying neural dynamics such as the number and degree of independence of oscillating neuronal networks. EEG complexity can be estimated using measures derived from nonlinear dynamic systems theory. Variations in such measures have been shown to be associated with normal individual differences in cognition and some neuropsychiatric disorders. Despite the increasing use of EEG complexity measures for the study of normal and abnormal brain functioning, little is known about genetic and environmental influences on these measures. Using the pointwise dimension (PD2) algorithm, this study assessed heritability of EEG complexity at rest in a sample of 214 young female twins consisting of 51 monozygotic (MZ) and 56 dizygotic (DZ) pairs. In MZ twins, intrapair correlations were high and statistically significant; in DZ twins, correlations were substantially smaller. Genetic analyses using linear structural equation modeling revealed high and significant heritability of EEG complexity: 62-68% in the eyes-closed condition, and 46-60% in the eyes-open condition. Results suggest that individual differences in the complexity of resting electrocortical dynamics are largely determined by genetic factors. Neurophysiological mechanisms mediating genetic variation in EEG complexity may include the degree of structural connectivity and functional differentiation among cortical neuronal assemblies.