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Recent advancements in the field of magnetic resonance imaging (MRI) have enabled large-scale collaboration among clinicians and researchers for neuroimaging tasks. However, researchers are often forced to use outdated and slow software to anonymize MRI images for publication. These programs specifically perform expensive mathematical operations over 3D images that rapidly slow down anonymization speed as an image's volume increases in size. In this paper, we introduce DeepDefacer, an application of deep learning to MRI anonymization that uses a streamlined 3D U-Net network to mask facial regions in MRI images with a significant increase in speed over traditional de-identification software. We train DeepDefacer on MRI images from the Brain Development Organization (IXI) and International Consortium for Brain Mapping (ICBM) and quantitatively evaluate our model against a baseline 3D U-Net model with regards to Dice, recall, and precision scores. We also evaluate DeepDefacer against Pydeface, a traditional defacing application, with regards to speed on a range of CPU and GPU devices and qualitatively evaluate our model's defaced output versus the ground truth images produced by Pydeface. We provide a link to a PyPi program at the end of this manuscript to encourage further research into the application of deep learning to MRI anonymization.