Patients with scarring of the liver (cirrhosis) and portal hypertension (elevated blood pressure in the liver vasculature) can develop esophageal varices (dilated veins). These have an increased risk of bleeding each year. Current recommendations are to prevent bleeding of medium or large varices (when there is no history of bleeding) by starting a blood pressure lowering agent known as a non-selective beta-blocker. Alternatively, rubber bands can be placed on medium to large varices to prevent bleeding (endoscopic variceal band ligation). Using both therapies at the same time has not been studied. In this study, we hope to determine if the use of combination therapy with endoscopic variceal band ligation and beta blockers is more effective than using beta blockers alone to prevent the first bleeding episode from the varices (dilated veins). The efficacy, ability to tolerate, and cost-effectiveness of these two treatment strategies will be compared.