Specific Language Impairment (SLI) has been explained by two broad classes of hypotheses, which posit either a deficit specific to grammar, or a non-linguistic processing impairment. Here we advance an alternative perspective. According to the Procedural Deficit Hypothesis (PDH), SLI can be largely explained by the abnormal development of brain structures that constitute the procedural memory system. This system, which is composed of a network of interconnected structures rooted in frontal/basal-ganglia circuits, subserves the learning and execution of motor and cognitive skills. Crucially, recent evidence also implicates this system in important aspects of grammar. The PDH posits that a significant proportion of individuals with SLI suffer from abnormalities of this brain network, leading to impairments of the linguistic and non-linguistic functions that depend on it. In contrast, functions such as lexical and declarative memory, which depend on other brain structures, are expected to remain largely spared. Evidence from an in-depth retrospective examination of the literature is presented. It is argued that the data support the predictions of the PDH, and particularly implicate Broca’s area within frontal cortex, and the caudate nucleus within the basal ganglia. Finally, broader implications are discussed, and predictions for future research are presented. It is argued that the PDH forms the basis of a novel and potentially productive perspective on SLI.