For decades, a major underlying assumption behind theories of sentence comprehension has been that the parser only entertains analyses that are grammatically consistent with all words encountered in the sentence so far. A dramatic challenge to this self-consistency assumption came from two self-paced reading experiments in English (Tabor et al., 2004). Using a syntactic and a semantic manipulation, Tabor et al. found that participants read a string of words more slowly if the string could locally form a grammatical structure that is ungrammatical given the preceding words. In the years since, such local coherence effects, and in particular syntactic local coherence effects, have generated much debate about the nature of human sentence parsing, and have become a central explanandum for psycholinguistic theories. Despite this attention, to our knowledge no one has directly attempted to replicate the claimed effects. Here, we present a large-sample replication attempt using the original Tabor et al. syntactic and semantic local coherence design using two methods (self-paced reading and bidirectional self-paced reading). A Bayes factor analysis shows evidence against a syntactic local coherence effect, and at best moderate evidence for a semantic local coherence effect. Our results suggest that the original effect sizes, especially for the much-debated syntactic local coherence effect, are likely to be overestimates due to low power in the original Tabor et al. (2004) study. An important implication for psycholinguistic theory is that the challenge to self-consistency posed by local coherence effects is not as strong as previously believed. Our results are therefore inconsistent with theories that predict local coherence effects.