Communication difficulties in autism spectrum disorder (ASD) involve a speech reception deficit, whose biological causes are not yet identified. This deficit could denote atypical neuronal ensemble activity, as reflected by neural oscillations. Atypical cross-frequency oscillation coupling in particular could disrupt the possibility to jointly track and predict dynamic acoustic stimuli, a dual process that is essential for speech comprehension. Whether such oscillation anomalies can already be found in very young children with ASD, and with what specificity they relate to individual language reception capacity is unknown. In this study, neural activity was collected using EEG in 64 very young children with and without ASD (mean age 3) while they were exposed to naturalistic-continuous speech via an age-appropriate cartoon. EEG power typically associated with phrase-level chunking (delta, 1-3Hz), phonemic encoding (low-gamma, 25-35Hz) and top-down control (beta, 12-20Hz) was markedly reduced in ASD relative to typically developing (TD) children. Speech neural-tracking by delta and theta oscillations was also weaker in ASD than TD children. Critically, children with ASD exhibited slightly atypical theta/gamma coupling (PAC) involving a higher-than-normal gamma frequency, and markedly atypical beta/gamma PAC. Even though many oscillation features were atypical in our sample of 31 very young children with ASD, the beta/gamma coupling anomaly was the single best predictor of individual speech reception difficulties. These findings suggest that early interventions targeting the normalization of low-gamma and low-beta activity, might help young children with ASD to engage more in oral interactions.