The ability to rapidly process speech sounds is integral not only for processing other's speech, but also for auditory processing of one's own speech, which allows for maintenance of speech accuracy. Deficits in rapid auditory processing have been demonstrated in autistic individuals, particularly those with language impairment. We examined rapid auditory processing for speech sounds in relation to performance on a battery of verbal communication measures to determine which aspects of verbal communication were associated with cortical auditory processing in a sample of individuals with autism. Participants were 57 children and adolescents (40 male and 17 female) ages 5-18 who were diagnosed with an Autism Spectrum Disorder (ASD). Rapid auditory processing of speech sounds was measured via a magnetoencephalographic (MEG) index of the quality of the auditory evoked response to the second of two differing speech sounds ("Ga" / "Da") presented in rapid succession. Verbal communication abilities were assessed on standardized clinical measures of overall expressive and receptive language, vocabulary, articulation, and phonological processing. Associations between cortical measures of left- and right-hemisphere rapid auditory processing and verbal communication measures were examined. Rapid auditory processing of speech sounds was significantly associated with speech articulation bilaterally (r = 0.463, p = 0.001 for left hemisphere and r = 0.328, p = 0.020 for right hemisphere). In addition, rapid auditory processing in the left hemisphere was significantly associated with overall expressive language abilities (r = 0.354, p = 0.013); expressive (r = 0.384, p = 0.005) vocabulary; and phonological memory (r = 0.325, p = 0.024). Phonological memory was found to mediate the relationship between rapid cortical processing and receptive language. These results demonstrate that impaired rapid auditory processing for speech sounds is associated with dysfunction in verbal communication in ASD. The data also indicate that intact rapid auditory processing may be necessary for even basic communication skills that support speech production, such as phonological memory and articulatory control.