Humans are highly adept at processing speech. Recently, it has been shown that slow temporal information in speech (i.e., the envelope of speech) is critical for speech comprehension. Furthermore, it has been found that evoked electric potentials in human cortex are correlated with the speech envelope. However, it has been unclear whether this essential linguistic feature is encoded differentially in specific regions, or whether it is represented throughout the auditory system. To answer this question, we recorded neural data with high temporal resolution directly from the cortex while human subjects listened to a spoken story. We found that the gamma activity in human auditory cortex robustly tracks the speech envelope. The effect is so marked that it is observed during a single presentation of the spoken story to each subject. The effect is stronger in regions situated relatively early in the auditory pathway (belt areas) compared to other regions involved in speech processing, including the superior temporal gyrus (STG) and the posterior inferior frontal gyrus (Broca's region). To further distinguish whether speech envelope is encoded in the auditory system as a phonological (speech-related), or instead as a more general acoustic feature, we also probed the auditory system with a melodic stimulus. We found that belt areas track melody envelope weakly, and as the only region considered. Together, our data provide the first direct electrophysiological evidence that the envelope of speech is robustly tracked in non-primary auditory cortex (belt areas in particular), and suggest that the considered higher-order regions (STG and Broca's region) partake in a more abstract linguistic analysis.