How do native speakers process texts with anomalous learner syntax? Second-language learners of Norwegian, and other verb-second (V2) languages, frequently place the verb in third position (e.g., *Adverbial-Subject-Verb), although it is mandatory for the verb in these languages to appear in second position (Adverbial-Verb-Subject). In an eye-tracking study, native Norwegian speakers read sentences with either grammatical V2 or ungrammatical verb-third (V3) word order. Unlike previous eye-tracking studies of ungrammaticality, which have primarily addressed morphosyntactic anomalies, we exclusively manipulate word order with no morphological or semantic changes. We found that native speakers reacted immediately to ungrammatical V3 word order, indicated by increased fixation durations and more regressions out on the subject, and subsequently on the verb. Participants also recovered quickly, already on the following word. The effects of grammaticality were unaffected by the length of the initial adverbial. The study contributes to future models of sentence processing which should be able to accommodate various types of “noisy” input, that is, non-standard variation. Together with new studies of processing of other L2 anomalies in Norwegian, the current findings can help language instructors and students prioritize which aspects of grammar to focus on.