We have developed a prototype hexagonal light concentrator for the Large-Sized Telescopes of the Cherenkov Telescope Array. To maximize the photodetection efficiency of the focal-plane camera pixels for atmospheric Cherenkov photons and to lower the energy threshold, a specular film with a very high reflectance of 92-99% has been developed to cover the inner surfaces of the light concentrators. The prototype has a relative anode sensitivity (which can be roughly regarded as collection efficiency) of about 95 to 105% at the most important angles of incidence. The design, simulation, production procedure, and performance measurements of the light-concentrator prototype are reported.