Elite Controller and ART-treated HIV+ Statin Versus ASA Treatment Intervention Study

Background: \- The immune system protects the body from infection. But it can also cause harm. For example, the clotting system makes blood clot and protects from bleeding. But blood clots are sometimes harmful. People with human immunodeficiency virus (HIV) infection have increased inflammation and clotting. This may increase their risk for diseases like stroke or heart attack. Researchers want to know how aspirin or HMG-CoA reductase inhibitors (so-called statin medications) affect the immune and clotting systems of people with HIV. Aspirin is a medicine to decrease clotting. Statins are medications given to lower cholesterol and decrease inflammation. Objectives: \- To see how aspirin or statins change immune and clotting systems in people with HIV. Eligibility: \- Adults 18 and older with HIV and a low viral load, not on aspirin or a statin medication. They must also have either: (1) never taken anti-HIV medications (ARVs), have a suppressed viral load, have stable CD4 counts, and never had an opportunistic infection; or (2) been taking ARVs for 5 continuous years and have a suppressed viral load for more than 3 years. Design: * Participants will be screened with medical history, physical exam, and blood and lab tests. * Participants will repeat screening tests and have an MRI. An MRI is a way to visualize blood vessels in the neck and head. Participants will lie on a table that slides in and out of a cylinder surrounded by a magnetic field. * Participants will take either study drug once daily for 9 months. * Participants will have a blood procedure twice. Blood will be removed through a needle in one arm and circulated through a machine that removes white blood cells. The blood, minus white blood cells, is returned through a needle in the other arm. * All participants will be observed for 3 months before and after treatment.