Acute coronary syndrome (ACS) is a serious and life threatening condition. Following an acute coronary syndrome event patients are at risk of important additional clinical events such as death, myocardial infarction, and stroke. Six months after patients present with an index event of ST-segment myocardial infarction, approximately 15% will either have died or had another episode of myocardial ischemia, and a similar situation exists for non-ST-segment elevation myocardial infarction/unstable angina patients. This randomized; double-blind; placebo controlled study will evaluate the efficacy and safety of rivaroxaban in addition to standard care in patients with a recent ACS. Patients will be given rivaroxaban (2.5 mg twice daily or 5 mg twice daily) or placebo (twice daily) in addition to standard care.