The purpose of this randomized, multi-site, clinical trial is to determine whether intensive therapy consisting of cholesterol-lowering statin drugs plus apheresis to cleanse the blood of low-density lipoprotein (LDL) cholesterol is more effective than statin therapy alone in reducing plaque volume in heart arteries of patients who have already suffered an acute coronary syndrome (ACS). The study will also investigate whether this intensive approach can help increase the presence of endothelial progenitor cells (EPC), stem cells that have been shown to reduce CV events in ACS patients. This study has two phases and FDA approval for phase II has been received and all information has been updated to reflect PREMIER Phase II.