There have been increasing interests in the robotics community in building smaller and more agile autonomous micro aerial vehicles (MAVs). In particular, the monocular visual-inertial system (VINS) that consists of only a camera and an inertial measurement unit (IMU) forms a great minimum sensor suite due to its superior size, weight, and power (SWaP) characteristics. In this paper, we present a tightly-coupled nonlinear optimization-based monocular VINS estimator for autonomous rotorcraft MAVs. Our estimator allows the MAV to execute trajectories at 2 m/s with roll and pitch angles up to 30 degrees. We present extensive statistical analysis to verify the performance of our approach in different environments with varying flight speeds.