It has been a matter of debate whether the specifically human capacity to process syntactic information draws on attentional resources or is automatic. To address this issue, we recorded neurophysiological indicators of syntactic processing to spoken sentences while subjects were distracted to different degrees from language processing. Subjects were either passively distracted, by watching a silent video film, or their attention was actively streamed away from the language input by performing a demanding acoustic signal detection task. An early index of syntactic violations, the syntactic Mismatch Negativity (sMMN), distinguished between grammatical and ungrammatical speech even under strongest distraction. The magnitude of the early sMMN (at <150ms) was unaffected by attention load of the distraction task. The independence of the early syntactic brain response of attentional distraction provides neurophysiological evidence for the automaticity of syntax and for its autonomy from other attention-demanding processes, including acoustic stimulus discrimination. The first attentional modulation of syntactic brain responses became manifest at a later stage, at approximately 200ms, thus demonstrating the narrowness of the early time window of syntactic autonomy. We discuss these results in the light of modular and interactive theories of cognitive processing and draw inferences on the automaticity of both the cognitive MMN response and certain grammar processes in general.