Aerial insects can effortlessly navigate dense vegetation, whereas similarly sized aerial robots typically depend on offboard sensors and computation to maintain stable flight. This disparity restricts insect-scale robots to operation within motion capture environments, substantially limiting their applicability to tasks such as search-and-rescue and precision agriculture. In this work, we present a 1.29-gram aerial robot capable of hovering and tracking trajectories with solely onboard sensing and computation. The combination of a sensor suite, estimators, and a low-level controller achieved centimeter-scale positional flight accuracy. Additionally, we developed a hierarchical controller in which a human operator provides high-level commands to direct the robot's motion. In a 30-second flight experiment conducted outside a motion capture system, the robot avoided obstacles and ultimately landed on a sunflower. This level of sensing and computational autonomy represents a significant advancement for the aerial microrobotics community, further opening opportunities to explore onboard planning and power autonomy.