- Age = 45 years. - Clinical diagnosis of ischemic stroke + brain imaging to rule out hemorrhagic stroke. - Modified Rankin Scale (MRS) score = 4. - Ability to be randomized within 3 to 180 days after stroke onset. - ESUS, defined as all of the following: - Stroke detected by CT or MRI that is not lacunar. Lacunar is defined as a subcortical (this includes pons and midbrain) infarct in the distribution of the small, penetrating cerebral arteries whose largest dimension is =1.5 cm on CT or =2.0 cm on MRI diffusion images/<1.5 cm on T2 weighted MR images. The following are not considered lacunes: multiple simultaneous small deep infarcts, lateral medullary infarcts, and cerebellar infarcts. Patients with a clinical lacunar stroke syndrome and no infarct on imaging are excluded. - Absence of extracranial or intracranial atherosclerosis causing =50 percent luminal stenosis of the artery supplying the area of ischemia. Patients must undergo vascular imaging of the extracranial and intracranial vessels using either catheter angiography, CT angiogram (CTA), MR angiogram (MRA), or ultrasound, as considered appropriate by the treating physician and local principal investigator. - No major-risk cardioembolic source of embolism, including intracardiac thrombus, mechanical prosthetic cardiac valve, atrial myxoma or other cardiac tumors, moderate or severe mitral stenosis, myocardial infarction within the last 4 weeks, left ventricular ejection fraction <30 percent, valvular vegetations, or infective endocarditis). Patent foramen ovale is not an exclusion. All patients must undergo electrocardiogram, transthoracic or transesophageal echocardiography (TTE or TEE) and at least 24 hours of cardiac rhythm monitoring (Holter monitor or telemetry or equivalent). Additional cardiac imaging, such as cardiac MRI, or cardiac CT will be performed at the discretion of the local treating physician and principal investigator. Additional cardiac rhythm monitoring, such as monitored cardiac outpatient telemetry (MCOT) or an implanted cardiac monitor, will be at the discretion of the treating physician and local principal investigator. - No other specific cause of stroke identified, such as arteritis, dissection, migraine, vasospasm, drug abuse, or hypercoagulability. Special testing, such as toxicological screens, serological testing for syphilis, and tests for hypercoagulability, will be performed at the discretion of the treating physician and local principal investigator.

- History of atrial fibrillation (AF), AF on 12-lead ECG, or any AF of any duration during heart-rhythm monitoring prior to randomization. - Clear indication for treatment-dose anticoagulant therapy, such as venous thromboembolism or a mechanical heart valve. - Need for antiplatelet agent, such as aspirin or clopidogrel - History of spontaneous intracranial hemorrhage. - Chronic kidney disease with serum creatinine =2.5 mg/dL.For Canadian sites only, estimated creatinine clearance (eCrCl) <15 mL/min is also an exclusion criterion. - Active hepatitis or hepatic insufficiency with Child-Pugh score B or C. - Clinically significant bleeding diathesis. - Unresolved anemia (hemoglobin <9 g/dL) or thrombocytopenia (<100 x 10E9/L). - Clinically significant gastrointestinal bleeding within the past year (e.g., not due to external hemorrhoids). - At risk for pregnancy: premenopausal or postmenopausal woman within 12 months of last menses without a negative pregnancy test or not committing to adequate birth control, which includes an oral contraceptive, two methods of barrier birth control such as condom with or without spermicidal lubricant + diaphragm, or abstinence. - Known allergy or intolerance to aspirin or apixaban. - Concomitant participation in another clinical trial involving a drug or acute stroke intervention. - Considered by the investigator to have a condition that precludes follow-up or safe participation in the trial. - Inability of either participant or surrogate to provide written, informed consent for trial participation.