Participating countries: France Objectives Principal objective To evaluate, in HIV-1 infected patients receiving effective antiretroviral therapy, the effect of the addition of Rosuvastatin (dose of 20mg/day) for 3 months, on CD8 T cell activation as assessed by the proportion of peripheral CD8 T cells that co-express the activation markers CD38 and HLA-DR Secondary objectives To evaluate the effect of Rosuvastatin administration on residual CD4 and CD8 T cell activation To evaluate the effect of Rosuvastatin administration on the main serum soluble biomarkers of activation (CRP- HS, D-dimers, IL-6 and soluble CD14) To evaluate the effect of Rosuvastatin administration on CD4 T-cell count and on the CD4/CD8 T-cell ratio To study the relationship between the level of immune activation and the level of residual HIV replication in plasma To study the effect of Rosuvastatin administration on lipid profiles and the correlation between the HDL cholesterol and the CD4/CD8 T-cell ratio To evaluate the tolerance of Rosuvastatin at the dose of 20 mg/day