Ultrasound localization microscopy has enabled super-resolution vascular imaging through precise localization of individual ultrasound contrast agents (microbubbles) across numerous imaging frames. However, analysis of high-density regions with significant overlaps among the microbubble point spread responses yields high localization errors, constraining the technique to low-concentration conditions. As such, long acquisition times are required to sufficiently cover the vascular bed. In this work, we present a fast and precise method for obtaining super-resolution vascular images from high-density contrast-enhanced ultrasound imaging data. This method, which we term Deep Ultrasound Localization Microscopy (Deep-ULM), exploits modern deep learning strategies and employs a convolutional neural network to perform localization microscopy in dense scenarios, learning the nonlinear image-domain implications of overlapping RF signals originating from such sets of closely spaced microbubbles. Deep-ULM is trained effectively using realistic on-line synthesized data, enabling robust inference in-vivo under a wide variety of imaging conditions. We show that deep learning attains super-resolution with challenging contrast-agent densities, both in-silico as well as in-vivo. Deep-ULM is suitable for real-time applications, resolving about 70 high-resolution patches (128×128 pixels) per second on a standard PC. Exploiting GPU computation, this number increases to 1250 patches per second.