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Autonomous drone racing competitions are a proxy to improve unmanned aerial vehicles' perception, planning, and control skills. The recent emergence of autonomous nano-sized drone racing imposes new challenges, as their form factor heavily restricts the resources available onboard, including memory, computation, and sensors. This letter describes the methodology and technical implementation of the system winning the first autonomous nano-drone racing international competition: the “IMAV 2022 Nanocopter AI Challenge.” We developed a fully onboard deep learning approach for visual navigation trained only on simulation images to achieve this goal. Our approach includes a convolutional neural network for obstacle avoidance, a sim-to-real dataset collection procedure, and a navigation policy that we selected, characterized, and adapted through simulation and actual in-field experiments. Our system …