Despite a bias of T lymphocytes toward the CD8+ phenotype in CLL patients [3, 4], the killing activity of cytotoxic T lymphocytes (CTLs), the CD8+ effector T cells specialized to eliminate tumor cells [5, 6], is defective, mainly as the result of high and sustained expression of inhibitory receptors such as Programmed cell Death protein (PD)-1, Cytotoxic T-Lymphocyte Antigen 4 (CTLA-4) and Lymphocyte-activation gene 3 (LAG-3) [7, 8]. This evidence concerns the gene CTLA4 and B-cell chronic lymphocytic leukemia.