Many people with HIV fail to regain normal CD4 counts despite effectively suppressing HIV replication with medications. Blocking the "co-receptor" for HIV might decrease inflammation of the immune system, potentially providing an immune benefit. The goal of the current trial is to determine whether adding maraviroc, a new CCR5 "co-receptor" blocker, decreases inflammation, providing an immune benefit for patients with low CD4 counts despite undetectable viral loads on HIV medications.