What psychological and linguistic processes allow one to go beyond the literal meaning of a sentence and infer what was meant but not said (“reading between the lines”)? Theorists have differed as to whether these phenomena are driven by complex, online inference processes or by relatively rote rules. The present study uses ERP to explore the cognitive and neural mechanisms involved in scalar implicature (the inference that, e.g., “some” indicates “some but not all”), a test case that has been subject to considerable behavioral research but limited neuropsychological research. Our results challenge both rote-processing and rich-inference accounts. We provide the first ERP results showing that scalar implicature processing depends on context, challenging rote-processing theories of implicature. However, we also fail to find evidence of a processing cost associated with implicature processing, as predicted by many rich-inference accounts. These results point to a novel conceptualization of pragmatic processing in scalar implicature.