Abstract: The ASTEP (Antarctica Search for Transiting ExoPlanets) program was originally aimed at probing the quality of the Dome C, Antarctica for the discovery and characterization of exoplanets by photometry. In the first year of operation of the 40 cm ASTEP 400 telescope (austral winter 2010), we targeted the known transiting planet WASP-19b in order to try to detect its secondary transits in the visible. This is made possible by the excellent sub-millimagnitude precision of the binned data. The WASP-19 system was observed during 24 nights in May 2010. The photometric variability level due to starspots is about 1.8% (peak-to-peak), in line with the SuperWASP data from 2007 (1.4%) and larger than in 2008 (0.07%). We find a rotation period of WASP-19 of 10.7 +/- 0.5 days, in agreement with the SuperWASP determination of 10.5 +/- 0.2 days. Theoretical models show that this can only be explained if tidal dissipation in the star is weak, i.e. the tidal dissipation factor Q'star > 3.10^7. Separately, we find evidence for a secondary eclipse of depth 390 +/- 190 ppm with a 2.0 sigma significance, a phase consistent with a circular orbit and a 3% false positive probability. Given the wavelength range of the observations (420 to 950 nm), the secondary transit depth translates into a day side brightness temperature of 2690(-220/+150) K, in line with measurements in the z' and K bands. The day side emission observed in the visible could be due either to thermal emission of an extremely hot day side with very little redistribution of heat to the night side, or to direct reflection of stellar light with a maximum geometrical albedo Ag=0.27 +/- 0.13. We also report a low-frequency oscillation well in phase at the planet orbital period, but with a lower-limit amplitude that could not be attributed to the planet phase alone, and possibly contaminated with residual lightcurve trends.