Segmentation of additive manufacturing (AM) defects in X-ray Computed Tomography (XCT) images is challenging, due to the poor contrast, small sizes and variation in appearance of defects. Automatic segmentation can, however, provide quality control for additive manufacturing. Over recent years, three-dimensional convolutional neural networks (3D CNNs) have performed well in the volumetric segmentation of medical images. In this work, we leverage techniques from the medical imaging domain and propose training a 3D U-Net model to automatically segment defects in XCT images of AM samples. This work not only contributes to the use of machine learning for AM defect detection but also demonstrates for the first time 3D volumetric segmentation in AM. We train and test with three variants of the 3D U-Net on an AM dataset, achieving a mean intersection of union (IOU) value of 88.4%.