Complex psychiatric disorders are resistant to whole-genome analysis due to genetic and etiological heterogeneity. Variation in resting electroencephalogram (EEG) is associated with common, complex psychiatric diseases including alcoholism, schizophrenia, and anxiety disorders, although not diagnostic for any of them. EEG traits for an individual are stable, variable between individuals, and moderately to highly heritable. Such intermediate phenotypes appear to be closer to underlying molecular processes than are clinical symptoms, and represent an alternative approach for the identification of genetic variation that underlies complex psychiatric disorders. We performed a whole-genome association study on alpha (alpha), beta (beta), and theta (theta) EEG power in a Native American cohort of 322 individuals to take advantage of the genetic and environmental homogeneity of this population isolate. We identified three genes (SGIP1, ST6GALNAC3, and UGDH) with nominal association to variability of theta or alpha power. SGIP1 was estimated to account for 8.8% of variance in power, and this association was replicated in US Caucasians, where it accounted for 3.5% of the variance. Bayesian analysis of prior probability of association based upon earlier linkage to chromosome 1 and enrichment for vesicle-related transport proteins indicates that the association of SGIP1 with theta power is genuine. We also found association of SGIP1 with alcoholism, an effect that may be mediated via the same brain mechanisms accessed by theta EEG, and which also provides validation of the use of EEG as an endophenotype for alcoholism.