The Cherenkov Telescope Array (CTA) will be the worlds first open observatory for very high energy gamma-rays. Around a hundred telescopes of different sizes will be used to detect the Cherenkov light that results from gamma-ray induced air showers in the atmosphere. Amongst them, a large number of Small Size Telescopes (SST), with a diameter of about 4 m, will assure an unprecedented coverage of the high energy end of the electromagnetic spectrum (above ~1TeV to beyond 100 TeV) and will open up a new window on the non-thermal sky. Several concepts for the SST design are currently being investigated with the aim of combining a large field of view (~9 degrees) with a good resolution of the shower images, as well as minimizing costs. These include a Davies-Cotton configuration with a Geiger-mode avalanche photodiode (GAPD) based camera, as pioneered by FACT, and a novel and as yet untested design based on the Schwarzschild-Couder configuration, which uses a secondary mirror to reduce the plate-scale and to allow for a wide field of view with a light-weight camera, e.g. using GAPDs or multi-anode photomultipliers. One objective of the GATE (Gamma-ray Telescope Elements) programme is to build one of the first Schwarzschild-Couder prototypes and to evaluate its performance. The construction of the SST-GATE prototype on the campus of the Paris Observatory in Meudon is under way. We report on the current status of the project and provide details of the opto-mechanical design of the prototype, the development of its control software, and simulations of its expected performance.