ASTEP South is the first phase of the ASTEP project that aims to determine the quality of Dome C as a site for future photometric searches for transiting exoplanets and discover extrasolar planets from the Concordia base in Antarctica. ASTEP South consists of a front-illuminated 4k × 4k CCD camera, a 10 cm refractor, and a simple mount in a thermalized enclosure. A double-glass window is used to reduce temperature variations and the associated turbulence on the optical path. The telescope is fixed and observes a 4° × 4° field of view centered on the celestial South pole. With this design, A STEP South is very stable and observes with low and constant airmass, both being important issues for photometric precision. We present the project, we show that enough stars are present in our field of view to allow the detection of one to a few transiting giant planets, and that the photometric precision of the instrument should be a few mmag for stars brighter than magnitude 12 and better than 10 mmag for stars of magnitude 14 or less.