Hierarchical sentence structure plays a role in word-by-word human sentence comprehension, but it remains unclear how best to characterize this structure and unknown how exactly it would be recognized in a step-by-step process model. With a view towards sharpening this picture, we model the time course of hemodynamic activity within the brain during an extended episode of naturalistic language comprehension using Combinatory Categorial Grammar (CCG). CCG has well-defined incremental parsing algorithms, surface compositional semantics, and can explain long-range dependencies as well as complicated cases of coordination. We find that CCG-derived predictors improve a regression model of fMRI time course in six language-relevant brain regions, over and above predictors derived from context-free phrase structure. Adding a special Revealing operator to CCG parsing, one designed to handle right-adjunction, improves the fit in three of these regions. This evidence for CCG from neuroimaging bolsters the more general case for mildly context-sensitive grammars in the cognitive science of language.