The ability to comprehend meaningful phrases is an essential component of language. Here we evaluate a minimal compositional scheme – the ‘red-boat’ paradigm – using intracranial recordings to map the process of semantic composition in phrase structure comprehension. 18 human participants, implanted with penetrating depth or surface subdural intracranial electrode for the evaluation of medically refractory epilepsy, were presented with auditory recordings of adjective-noun, pseudoword-noun and adjective-pseudoword phrases before being presented with a colored drawing, and were asked to judge whether the phrase matched the object presented. Significantly greater broadband gamma activity (70-150Hz) occurred in temporo-occipital junction (TOJ) and posterior middle temporal gyrus (pMTG) for pseudowords over words (300-700ms post-onset) in both first- and second-word positions. Greater inter-trial phase coherence (8-12Hz) was found for words than for pseudowords in posterior superior temporal gyrus (pSTG). Isolating phrase structure sensitivity, we identified a portion of TOJ and posterior superior temporal sulcus (pSTS) that showed increased gamma activity for phrase composition than for non-composition, while left anterior temporal lobe (ATL) showed greater low frequency (2-15Hz) activity for phrase composition, likely coordinating distributed semantic representations. Greater functional connectivity between pSTS-TOJ and pars triangularis, and between pSTS-TOJ and ATL, was also found for phrase composition. STG, ATL and pars triangularis were found to encode anticipation of composition in the beta band (15-30Hz), and alpha (8-12Hz) power increases in ATL were also linked to anticipation. These results indicate that pSTS-TOJ appears to be crucial hub in the network responsible for the retrieval and computation of minimal phrases, and that anticipation of such composition is encoded in fronto-temporal regions.