Palifermin is a modified version of a naturally occurring human growth factor that is currently approved by the FDA to treat blood cancers. The purpose of this study is to determine whether palifermin can increase CD4 counts in treatment-experienced HIV infected adults.

Antiretroviral therapy (ART) has dramatically improved the clinical outcome for HIV infected adults; however, some people on potent ART experience poor recovery of CD4 counts despite maximum suppression of viral load. Such uncontrolled HIV infection is associated with the reduced ability by the human body to create new T cells (or thymopoiesis). HIV infected adults experiencing reduced thymopoiesis are at increased risk of clinical disease progression. The thymus is the primary site for CD4 cell development; research suggests that keratinocyte growth factor (KGF) may enhance thymus activity in individuals who exhibit reduced thymopoiesis. Palifermin is a modified version of the naturally occurring KGF that is approved to treat people with hematologic malignancies. The purpose of this study is to evaluate the safety and efficacy of palifermin in increasing CD4 counts, through enhanced thymopoiesis, in treatment-experienced HIV infected adults with suppressed viral loads but low CD4 counts. This study will last 24 weeks. Participants will be randomly assigned to one of four arms: * Arm A participants will receive placebo * Arm B participants will receive palifermin 20 mcg/kg * Arm C participants will receive palifermin 40 mcg/kg * Arm D participants will receive palifermin 60 mcg/kg Participants will receive intravenous doses of their assigned intervention on Days 1, 2, and 3. All participants must remain on their current ART regimen for the duration of the study. ART will not be provided by the study. There will be six study visits, and they will occur at Weeks 1, 2, 4, 8, 12, and 24. All visits will include a targeted physical exam and blood and urine collection.