Carotid ultrasound is a screening modality used by physicians to direct treatment in the prevention of ischemic stroke in high-risk patients. It is a time intensive process that requires highly trained technicians and physicians. Evaluation of a carotid ultrasound requires segmentation of the vessel wall, lumen, and plaque of the carotid artery. Convolutional neural networks are state of the art in image segmentation yet there are no previous methods to solve this problem on carotid ultrasounds. We evaluate here a U-net convolutional neural network for lumen segmentation from ultrasound images of the entire carotid system. We obtained de-identified images under IRB approval from 226 patients. We isolated the internal, external, and common carotid artery ultrasound images for these patients giving us a total of 2156 images. We manually segmented the vessel lumen in each image that we then use as ground truth. With our convolutional U-Net we obtained a 10-fold cross-validation accuracy of 94.3%. We see that the U-Net correctly segments the lumen even in the presence of significant plaque, calcified wall, and ultrasound shadowing, all of which make it difficult to outline the vessel. We also see that the common carotid artery vessels are easiest to segment with a 96.6% cross-validation accuracy whereas internal and external carotid are harder both with 92.7% and 91.9% cross-validation accuracies respectively. Our work here represents a first successful step towards the automated segmentation of the vessel lumen in carotid artery ultrasound images and is an important first step in creating a system that can independently evaluate carotid ultrasounds.