We provide evidence that children with Developmental Language Disorder (DLD) are impaired in predictive syntactic processing. In the current study, children listened passively to auditorily-presented sentences, where the critical condition included an unexpected “filled gap” in the direct object position of the relative clause verb. A filled gap is illustrated by the underlined phrase in “The zebra that the hippo kissed the camel on the nose…”, rather than the expected “the zebra that the hippo kissed [e] on the nose”, where [e] denotes the gap. Brain responses to the filled gap were compared to a control condition using adverb-relative clauses with identical substrings: “The weekend that the hippo kissed the camel on the nose [e]…”. Here, the same noun phrase is not unexpected because the adverb gap occurs later in the structure. We hypothesized that a filled gap would elicit a prediction error brain signal in the form of an early anterior negativity, as we have previously observed in adults. We found an early (bilateral) anterior negativity to the filled gap in a control group of children with Typical Development (TD), but the children with DLD exhibited no brain response to the filled gap during the same early time window. This suggests that children with DLD fail to predict that a relativized object should correspond to an empty position after the relative clause verb, suggesting an impairment in predictive processing. We discuss how this lack of a prediction error signal can interact with language acquisition and result in DLD.