The core human capacity of syntactic analysis involves a left hemisphere network involving left inferior frontal gyrus (LIFG) and posterior middle temporal gyrus (LMTG) and the anatomical connections between them. Here we use magnetoencephalography (MEG) to determine the spatio-temporal properties of syntactic computations in this network. Listeners heard spoken sentences containing a local syntactic ambiguity (e.g., "… landing planes …"), at the offset of which they heard a disambiguating verb and decided whether it was an acceptable/unacceptable continuation of the sentence. We charted the time-course of processing and resolving syntactic ambiguity by measuring MEG responses from the onset of each word in the ambiguous phrase and the disambiguating word. We used representational similarity analysis (RSA) to characterize syntactic information represented in the LIFG and left posterior middle temporal gyrus (LpMTG) over time and to investigate their relationship to each other. Testing a variety of lexico-syntactic and ambiguity models against the MEG data, our results suggest early lexico-syntactic responses in the LpMTG and later effects of ambiguity in the LIFG, pointing to a clear differentiation in the functional roles of these two regions. Our results suggest the LpMTG represents and transmits lexical information to the LIFG, which responds to and resolves the ambiguity.