The position of the grounding line of marine terminating glaciers, the boundary where glacier ice is no longer supported by the ground and starts floating, is a key parameter for a better understanding of glacier dynamics and better quantification of glacier mass balance. Grounding lines have so far been delineated by human interpreters from Differential Interferometric Synthetic Aperture Radar (D-InSAR) products. This is an arduous and time-consuming process that is not scalable for large-scale delineation from the ever-larger amount of remote-sensing data becoming available, which is necessary for a better understanding of glaciological processes. In order to solve this issue, we present a deep learning approach using a convolutional neural network with parallel atrous convolutions and an asymmetric encoding/decoding structure to successfully delineate thousands of grounding lines rapidly and accurately. Furthermore, the neural network outputs uncertainty estimates, which have so far been missing from grounding line delineations. Over the Getz Ice Shelf in West Antarctica, we find a mean difference of 232 meters, or 2.3 pixels, between automatic delineations and manual delineations on test data not used during training. The spread of differences is given by a median absolute deviation of 101 meters. The performance of the neural network is comparable to that of human interpreters, with manual delineations falling within the uncertainty range of automatic delineations. Similar differences exist between multiple manual delineations, with a slightly higher mean difference (268 meters) and a lower spread (median absolute deviation of 52 meters). We show our deep learning pipeline is easily generalizable and scalable to the entire ice sheet, revolutionizing the availability of grounding line delineations for glaciological studies.