The ASTEP project aims at detecting and characterizing transiting planets from Dome C, Antarctica, and qualifying this site for photometry in the visible. The first phase of the project, ASTEP South, is a fixed 10 cm diameter instrument pointing continuously towards the celestial South Pole. Observations were made almost continuously during 4 winters, from 2008 to 2011. The point-to-point RMS of 1-day photometric lightcurves can be explained by a combination of expected statistical noises, dominated by the photon noise up to magnitude 14. This RMS is large, from 2.5 mmag at R = 8 to 6% at R = 14, because of the small size of ASTEP South and the short exposure time (30 s). Statistical noises should be considerably reduced using the large amount of collected data. A 9.9-day period eclipsing binary is detected, with a magnitude R = 9.85. The 2-season lightcurve folded in phase and binned into 1,000 points has a RMS of 1.09 mmag, for an expected photon noise of 0.29 mmag. The use of the 4 seasons of data with a better detrending algorithm should yield a sub-millimagnitude precision for this folded lightcurve. Radial velocity follow-up observations reveal a F-M binary system. The detection of this 9.9-day period system with a small instrument such as ASTEP South and the precision of the folded lightcurve show the quality of Dome C for continuous photometric observations, and its potential for the detection of planets with orbital periods longer than those usually detected from the ground.