Intellectual functioning is a critical determinant of economic and personal productivity. Identifying early neural predictors of cognitive function in infancy will allow us to map the neurodevelopmental pathways that underpin individual differences in intellect. Here, in three different cohorts we investigate the association between a putative neurophysiological indicator of information encoding (change in frontal theta during a novel video) in infancy and later general cognitive outcome. In a discovery cohort of 12-month-old typically developing infants, we recorded EEG during presentation of dynamic movies of people and objects. Frontal theta power (3-6 Hz) significantly increased during the course of viewing each video. Critically, increase in frontal theta during viewing of a video was associated with a differential response to repetition of that specific video, confirming relation to learning. Further, individual differences in the magnitude of change in frontal theta power were related to concurrent nonverbal cognitive level. We then sought to extend this association in two independent samples enriched for variation in cognitive outcome due to the inclusion of infants at familial risk for autism. We observed similar patterns of theta EEG change at 12 months, and found a predictive relation to verbal and nonverbal cognitive skills measured at 2, 3 and 7 years of age. For the subset of high-risk infants later diagnosed with autism, infant theta EEG explained over 80% of the variance in nonverbal skills at age 3 years. We suggest that EEG theta change in infancy is an excellent candidate predictive biomarker that could yield substantial insight into the mechanisms that underlie individual differences in childhood intelligence, particularly in high risk populations.