This paper proposes a vision-based algorithm to autonomously track and chase a moving target with a small-size flying UAV. The challenging constraints associated with the UAV flight led us to consider a density-based representation of the object to track. The proposed approach to estimate the target's position, orientation and scale, is built on a robust color-based tracker using a multi-part representation. This object tracker can handle large displacements, occlusions and account for some image noise due to partial loss of wireless video link, thanks to the use of a particle filter. The information obtained from the visual tracker is then used to control the position and yaw angle of the UAV in order to chase the target. A hierarchical control scheme is designed to achieve the tracking task. Experiments on a quad-rotor UAV following a small moving car are provided to validate the proposed approach.