High-frequency cortical activity in humans and animals has been linked to a wide variety of higher cognitive processes. This research suggests that specific changes in neuronal synchrony occur during cognitive processing, distinguished by emergence of fast oscillations in the gamma frequency range. To determine whether the development of high-frequency brain oscillations can be related to the development of cognitive abilities, we studied the power spectra of resting EEG in children 16, 24 and 36 months of age. Individual differences in the distribution of frontal gamma power during rest were highly correlated with concurrent language and cognitive skills at all ages. Gamma power was also associated with attention measures; children who were observed as having better inhibitory control and more mature attention shifting abilities had higher gamma power density functions. We included a group of children with a family history of language impairment (FH+) and thus at higher risk for language disorders. FH+ children, as a group, showed consistently lower gamma over frontal regions than the well-matched FH- controls with no such family history (FH-). We suggest that the emergence of high-frequency neural synchrony may be critical for cognitive and linguistic development, and that children at risk for language impairments may lag in this process.