Previous research has established that readers' eye movements are sensitive to the difficulty with which a word is processed. One important factor that influences processing is the fit of a word within the wider context, including its plausibility. Here we explore the influence of plausibility in counterfactual language processing. Counterfactuals describe hypothetical versions of the world but are grounded in the implication that the described events are not true. We report an eye-tracking study that examined the processing of counterfactual premises that varied the plausibility of a described action and manipulated the narrative perspective ("you" vs. "he/she"). Results revealed a comparable pattern to previous plausibility experiments. Readers were sensitive to the inconsistent thematic relation in anomalous and implausible conditions. The fact that these anomaly detection effects were evident within a counterfactual frame suggests that participants were evaluating incoming information within the counterfactual world and did not suspend processing based on an inference about reality. Interestingly, perspective modulated the speed with which anomalous but not implausible words were detected.