Event-based vision sensors, such as the Dynamic Vision Sensor (DVS), do not output a sequence of video frames like standard cameras, but a stream of asynchronous events. An event is triggered when a pixel detects a change of brightness in the scene. An event contains the location, sign, and precise timestamp of the change. The high dynamic range and temporal resolution of the DVS, which is in the order of micro-seconds, make this a very promising sensor for high-speed applications, such as robotics and wearable computing. However, due to the fundamentally different structure of the sensor's output, new algorithms that exploit the high temporal resolution and the asynchronous nature of the sensor are required. In this paper, we address ego-motion estimation for an event-based vision sensor using a continuous-time framework to directly integrate the information conveyed by the sensor. The DVS pose trajectory is approximated by a smooth curve in the space of rigid-body motions using cubic splines and it is optimized according to the observed events. We evaluate our method using datasets acquired from sensor-in-the-loop simulations and onboard a quadrotor performing flips. The results are compared to the ground truth, showing the good performance of the proposed technique.