This paper is an initial step toward the realization of an aerial robot that can perform lateral physical work, such as drilling a hole or fastening a screw in a wall. Aerial robots are capable of high maneuverability and can provide access to locations that would be difficult or impossible for ground-based robots to reach. However, to fully utilize this mobility, systems would ideally be able to perform functional work in those locations, requiring the ability to exert lateral forces. To substantially improve a hovering vehicle’s ability to stably deliver large lateral forces, we propose the use of a versatile suction-based gripper that can establish pulling contact on featureless surfaces. Such contact enables access to environmental forces that can be used to further stabilize the vehicle and also increase the lateral force delivered to the surface through a possible secondary mechanism. This paper introduces the concept, describes the design of a new self-sealing suction cup based on a previous design, details the design of a gripper using those cups, and describes the arm and flight vehicle. It then evaluates the cup and gripper performance in several ways, culminating in physical grasping demonstrations using the arm and gripper, including one in the presence of simulated flight noise based on data from preliminary indoor flight experiments.