Prediction is a core computation in language, as humans use preceding context to implicitly make predictions about the upcoming word in a sentence. In order to do this, humans need some memory for context that is selective and adaptive. We take inspiration from the existing prefrontal cortex literature, in which computational models feature a biologically plausible gating mechanism that can actively maintain and rapidly update task-relevant information to improve performance on cognitive flexibility and working memory tasks. Here, we investigate the potential role of such gating mechanisms in maintaining context for prediction during real-time language processing. Using EEG data from a naturalistic story listening task, we first replicate previous findings that words of low predictability based on preceding context (high in surprisal) elicit larger N400 effects than predictable words. To study how gating may play a role in next-word prediction, we use a performance difference metric between language models with and without gating, which we show is sensitive to word-by-word working memory demand. We find that this gating metric is correlated with EEG amplitude in several later time windows after word onset, providing suggestions concerning the time course of context gating.