It has been previously reported that structural and functional brain connectivity in individuals with autism spectrum disorders (ASD) is atypical and may vary with age. However, to date, no measures of functional connectivity measured within the first 2 years have specifically associated with a later ASD diagnosis. In the present study, we analyzed functional brain connectivity in 14-month-old infants at high and low familial risk for ASD using electroencephalography (EEG). EEG was recorded while infants attended to videos. Connectivity was assessed using debiased weighted phase lag index (dbWPLI). At 36 months, the high-risk infants were assessed for symptoms of ASD. As a group, high-risk infants who were later diagnosed with ASD demonstrated elevated phase-lagged alpha-range connectivity as compared to both low-risk infants and high-risk infants who did not go on to ASD. Hyper-connectivity was most prominent over frontal and central areas. The degree of hyper-connectivity at 14 months strongly correlated with the severity of restricted and repetitive behaviors in participants with ASD at 3 years. These effects were not attributable to differences in behavior during the EEG session or to differences in spectral power. The results suggest that early hyper-connectivity in the alpha frequency range is an important feature of the ASD neurophysiological phenotype.