Inclusion Criteria:  History of peripheral artery disease (PAD) defined as:  Previous aorto-femoral bypass surgery, limb bypass surgery, or percutaneous transluminal angioplasty revascularization of the iliac or infra-inguinal arteries, or Previous limb or foot amputation for arterial vascular disease, or  History of intermittent claudication and one or more of the following:  An ankle/arm blood pressure (BP) ratio < 0.90, or Significant peripheral artery stenosis (≥50%) documented by angiography, or by duplex ultrasound Willing and able to provide written informed consent Age ≥65, or Age <65 and documented atherosclerosis or revascularization involving at least 2 vascular beds (lower extremity PAD, coronary artery disease, and/or carotid artery stenosis) Receiving aspirin therapy prior to enrollment  Exclusion Criteria:  High risk of bleeding Stroke within 1 month of any history of hemorrhagic or lacunar stroke Severe heart failure with known ejection fraction <30% or New York Heart Association (NYHA) class III or IV symptoms Estimated glomerular filtration rate <15 mL/min/1.73m2 Need for dual-antiplatelet therapy, other non-aspirin antiplatelet therapy, or oral anticoagulant therapy Known non-cardiovascular disease that is associated with poor prognosis (e.g. metastatic cancer) or that increases the risk of an adverse reaction to study interventions History of hypersensitivity or known contraindication to rivaroxaban or aspirin Systemic treatment with strong inhibitors of both CYP 3A4 and p-glycoprotein (e.g. systemic azole antimycotics, such as ketoconazole, and human immunodeficiency virus [HIV]-protease inhibitors, such as ritonavir), or strong inducers of CYP 3A4, i.e. rifampicin, rifabutin, phenobarbital, phenytoin, and carbamazepine Any known hepatic disease associated with coagulopathy Subjects who are pregnant, breastfeeding, or are of childbearing potential, and sexually active and not practicing an effective method of birth control (e.g. surgically sterile, prescription oral contraceptives, contraceptive injections, intrauterine device, double- barrier method, contraceptive patch, male partner sterilization) Concomitant participation in another study with investigational drug Known contraindication to any study related procedures