The Carotid Occlusion Surgery Study (COSS) is an NIH-funded, randomized clinical trial. In this study, we will determine if extracranial-intracranial (EC/IC) bypass surgery combined with best medical therapy can reduce subsequent ipsilateral ischemic stroke (fatal and non-fatal) at two years by 40%, despite perioperative stroke and death. Eligible participants must have internal carotid artery occlusion producing hemispheric symptoms within the previous 120 days and ipsilateral increased oxygen extraction fraction (OEF) measured by positron emission tomography (PET). Clinically eligible subjects will undergo PET. Those with increased OEF will be randomized equally to undergo EC/IC bypass or not. Follow-up is at one month and every three months for two years. For those with normal OEF, PET provides evidence of good prognosis on medical therapy alone. The study will pay for PET and for EC/IC bypass surgery.