This work deals with a moving target chasing mission of an aerial vehicle equipped with a vision sensor in a cluttered environment. In contrast to obstacle-free or sparse environments, the chaser should be able to handle collision and occlusion together with flight efficiency. In order to tackle these challenges in real-time, we introduce a metric for target visibility and propose a hierarchical chasing planner. In the first phase, we generate a sequence of waypoints and chasing corridors which ensure safety and optimize visibility. In the following phase, the corridors and waypoints are utilized as constraints and objective respectively in quadratic programming from which we complete a dynamically feasible trajectory for chasing. The proposed algorithm is tested in multiple dense environments. The simulator AutoChaser with full code implementation & GUI can be found in https://github.com/icsl-Jeon/traj_gen_vis and video is available at https://youtu.be/-2d3uDlYR_M.