A pervasive challenge in brain imaging is the presence of noise that hinders investigation of underlying neural processes, with Magnetoencephalography (MEG) in particular having very low Signal-to-Noise Ratio (SNR). The established strategy to increase MEG's SNR involves averaging multiple repetitions of data corresponding to the same stimulus. However, repetition of stimulus can be undesirable, because underlying neural activity has been shown to change across trials, and repeating stimuli limits the breadth of the stimulus space experienced by subjects. In particular, the rising popularity of naturalistic studies with a single viewing of a movie or story necessitates the discovery of new approaches to increase SNR. We introduce a simple framework to reduce noise in single-trial MEG data by leveraging correlations in neural responses across subjects as they experience the same stimulus. We demonstrate its use in a naturalistic reading comprehension task with 8 subjects, with MEG data collected while they read the same story a single time. We find that our procedure results in data with reduced noise and allows for better discovery of neural phenomena. As proof-of-concept, we show that the N400m's correlation with word surprisal, an established finding in literature, is far more clearly observed in the denoised data than the original data. The denoised data also shows higher decoding and encoding accuracy than the original data, indicating that the neural signals associated with reading are either preserved or enhanced after the denoising procedure.