We present deep and precise photometry (F435, F625W, F658N) of Omega Cen collected with the Advanced Camera for Surveys (ACS) on board the Hubble Space Telescope (HST). We have identified ~ 6,500 white dwarf (WD) candidates, and the ratio of WD and Main Sequence (MS) star counts is found to be at least a factor of two larger than the ratio of CO-core WD cooling and MS lifetimes. This discrepancy is not explained by the possible occurrence of a He-enhanced stellar population, since the MS lifetime changes by only 15% when changing from a canonical (Y=0.25) to a He-enhanced composition (Y=0.42). The presence of some He-core WDs seems able to explain the observed star counts. The fraction of He WDs required ranges from 10% to 80% depending on their mean mass and it is at least five times larger than for field WDs. The comparison in the Color Magnitude Diagram between theory and observations also supports the presence of He WDs. Empirical evidence indicates that He WDs have been detected in stellar systems hosting a large sample of extreme horizontal branch stars, thus suggesting that a fraction of red giants might avoid the He-core flash. Comment: 14 pages, 3 figures, accepted for publication to ApJ