We present an algorithm to estimate the rotational motion of an event camera. In contrast to traditional cameras, which produce images at a fixed rate, event cameras have independent pixels that respond asynchronously to brightness changes, with microsecond resolution. Our method leverages the type of information conveyed by these novel sensors (i.e., edges) to directly estimate the angular velocity of the camera, without requiring optical flow or image intensity estimation. The core of the method is a contrast maximization design. The method performs favorably against ground truth data and gyroscopic measurements from an Inertial Measurement Unit, even in the presence of very high-speed motions (close to 1000 deg/s).