This paper presents Navion, an energy-efficient accelerator for visual-inertial odometry (VIO) that enables autonomous navigation of miniaturized robots (e.g., nano drones), and virtual/augmented reality on portable devices. The chip uses inertial measurements and mono/stereo images to estimate the drone's trajectory and a 3D map of the environment. This estimate is obtained by running a state-of-the-art algorithm based on non-linear factor graph optimization, which requires large irregularly structured memories and heterogeneous computation flow. To reduce the energy consumption and footprint, the entire VIO system is fully integrated on chip to eliminate costly off-chip processing and storage. This work uses compression and exploits both structured and unstructured sparsity to reduce on-chip memory size by 4.1x. Parallelism is used under tight area constraints to increase throughput by 43%. The chip is fabricated in 65nm CMOS, and can process 752×480 stereo images at up to 171 fps and inertial measurements at up to 52 kHz, while consuming an average of 24mW. The chip is configurable to maximize accuracy, throughput and energy-efficiency across different environments. To the best of our knowledge, this is the first fully integrated VIO system in an ASIC.