Rapidly generating an optimal chasing motion of a drone to follow a dynamic target among obstacles is challenging due to numerical issues rising from multiple conflicting objectives and non-convex constraints. This study proposes to resolve the difficulties with a fast and reliable pipeline that incorporates 1) a target movement forecaster and 2) a chasing planner. They are based on a sample-and-check approach that consists of the generation of high-quality candidate primitives and the feasibility tests with a light computation load. We forecast the movement of the target by selecting an optimal prediction among a set of candidates built from past observations. Based on the prediction, we construct a set of prospective chasing trajectories which reduce the high-order derivatives, while maintaining the desired relative distance from the predicted target movement. Then, the candidate trajectories are tested on safety of the chaser and visibility toward the target without loose approximation of the constraints. The proposed algorithm is thoroughly evaluated in challenging scenarios involving dynamic obstacles. Also, the overall process from the target recognition to the chasing motion planning is implemented fully onboard on a drone, demonstrating real-world applicability.