Over the past decade, studies of naturalistic language processing where participants are scanned while listening to continuous text have flourished. Using word embeddings at first, then large language models, researchers have created encoding models to analyze the brain signals. Presenting these models with the same text as the participants allows to identify brain areas where there is a significant correlation between the functional magnetic resonance imaging (fMRI) time series and the ones predicted by the models' artificial neurons. One intriguing finding from these studies is that they have revealed highly symmetric bilateral activation patterns, somewhat at odds with the well-known left lateralization of language processing. Here, we report analyses of an fMRI dataset where we manipulate the complexity of large language models, testing 28 pretrained models from 8 different families, ranging from 124M to 14.2B parameters. First, we observe that the performance of models in predicting brain responses follows a scaling law, where the fit with brain activity increases linearly with the logarithm of the number of parameters of the model (and its performance on natural language processing tasks). Second, although this effect is present in both hemispheres, it is stronger in the left than in the right hemisphere. Specifically, the left-right difference in brain correlation follows a scaling law with the number of parameters. This finding reconciles computational analyses of brain activity using large language models with the classic observation from aphasic patients showing left hemisphere dominance for language.