Flying insects have evolved to develop efficient strategies to navigate in natural environments. Yet, studying them experimentally is difficult because of their small size and high speed of motion. Consequently, previous studies were limited to tethered flights, hovering flights, or restricted flights within confined laboratory chambers. Here, we report the development of a cable-driven parallel robot, named lab-on-cables, for tracking and interacting with a free-flying insect. In this approach, cameras are mounted on cables, so as to move automatically with the insect. We designed a reactive controller that minimizes the online tracking error between the position of the flying insect, provided by an embedded stereo-vision system, and the position of the moving lab, computed from the cable lengths. We validated the lab-on-cables with Agrotis ipsilon moths (ca. 2 centimeters long) flying freely up to 3 meters per second. We further demonstrated, using prerecorded trajectories, the possibility to track other insects such as fruit flies or mosquitoes. The lab-on-cables is relevant to free-flight studies and may be used in combination with stimulus delivery to assess sensory modulation of flight behavior (e.g., pheromone-controlled anemotaxis in moths).