A collision avoidance system based on simple digital cameras would help enable the safe integration of small UAVs into crowded, low-altitude environments. In this work, we present an obstacle avoidance system for small UAVs that uses a monocular camera with a hybrid neural network and path planner controller. The system is comprised of a vision network for estimating depth from camera images, a high-level control network, a collision prediction network, and a contingency policy. This system is evaluated on a simulated UAV navigating an obstacle course in a constrained flight pattern. Results show the proposed system achieves low collision rates while maintaining operationally relevant flight speeds.