The security infrastructure is ill-equipped to detect and deter the smuggling of non-explosive devices that enable terror attacks such as those recently perpetrated in western Europe. The detection of so-called "small metallic threats" (SMTs) in cargo containers currently relies on statistical risk analysis, intelligence reports, and visual inspection of X-ray images by security officers. The latter is very slow and unreliable due to the difficulty of the task: objects potentially spanning less than 50 pixels have to be detected in images containing more than 2 million pixels against very complex and cluttered backgrounds. In this contribution, we demonstrate for the first time the use of Convolutional Neural Networks (CNNs), a type of Deep Learning, to automate the detection of SMTs in fullsize X-ray images of cargo containers. Novel approaches for dataset augmentation allowed to train CNNs from-scratch despite the scarcity of data available. We report fewer than 6% false alarms when detecting 90% SMTs synthetically concealed in stream-of-commerce images, which corresponds to an improvement of over an order of magnitude over conventional approaches such as Bag-of-Words (BoWs). The proposed scheme offers potentially super-human performance for a fraction of the time it would take for a security officers to carry out visual inspection (processing time is approximately 3.5s per container image).