Event cameras are bio-inspired vision sensors that output pixel-level brightness changes instead of standard intensity frames. They offer significant advantages over standard cameras, namely a very high dynamic range, no motion blur, and a latency in the order of microseconds. We propose a novel, accurate tightly-coupled visual-inertial odom- etry pipeline for such cameras that leverages their outstanding properties to estimate the camera ego-motion in challenging conditions, such as high-speed motion or high dynamic range scenes. The method tracks a set of features (extracted on the image plane) through time. To achieve that, we consider events in overlapping spatio-temporal windows and align them using the current camera motion and scene structure, yielding motion-compensated event frames. We then combine these feature tracks in a keyframe- based, visual-inertial odometry algorithm based on nonlinear optimization to estimate the camera’s 6-DOF pose, velocity, and IMU biases. The proposed method is evaluated quantitatively on the public Event Camera Dataset [19] and significantly outperforms the state-of-the-art [28], while being computationally much more efficient: our pipeline can run much faster than real-time on a laptop and even on a smartphone processor. Fur- thermore, we demonstrate qualitatively the accuracy and robustness of our pipeline on a large-scale dataset, and an extremely high-speed dataset recorded by spinning an event camera on a leash at 850 deg/s.