The Cherenkov Telescope Array (CTA) is the next generation ground-based observatory for very high-energy (E>100 GeV) gamma-ray astronomy. It will integrate several tens of imaging atmospheric Cherenkov telescopes (IACTs) with different apertures into a single astronomical instrument. The US part of the CTA collaboration has proposed and is developing a novel IACT design with a Schwarzschild-Couder (SC) aplanatic two-mirror optical system. In comparison with the traditional single mirror Davies-Cotton IACT the SC telescope, by design, can accommodate a wider field-of-view, with significantly improved imaging resolution. In addition, the reduced plate scale of an SC telescope makes it compatible with highly integrated cameras assembled from silicon photo multipliers. In this submission we report on the status of the development of the SC optical system, which is part of the e ort to construct a full-scale prototype telescope of this type at the Fred Lawrence Whipple Observatory in southern Arizona.