Deep language models (DLMs) provide a novel computational paradigm for how the brain processes natural language. Unlike symbolic, rule-based models from psycholinguistics, DLMs encode words and their context as continuous numerical vectors. These “embeddings” are constructed by a sequence of layered computations to ultimately capture surprisingly sophisticated representations of linguistic structures. How does this layered hierarchy map onto the human brain during natural language comprehension? In this study, we used ECoG to record neural activity in language areas along the superior temporal gyrus and inferior frontal gyrus while human participants listened to a 30-minute spoken narrative. We supplied this same narrative to a high-performing DLM (GPT2-XL) and extracted the contextual embeddings for each word in the story across all 48 layers of the model. We next trained a set of linear encoding models to predict the temporally-evolving neural activity from the embeddings at each layer. We found a striking correspondence between the layer-by-layer sequence of embeddings from GPT2-XL and the temporal sequence of neural activity in language areas. In addition, we found evidence for the gradual accumulation of recurrent information along the linguistic processing hierarchy. However, we also noticed additional neural processes that took place in the brain, but not in DLMs, during the processing of surprising (unpredictable) words. These findings point to a connection between language processing in humans and DLMs where the layer-by-layer accumulation of contextual information in DLM embeddings matches the temporal dynamics of neural activity in high-order language areas.