The HIV-specific cytotoxic T lymphocyte (CTL) response is a critical component in controlling HIV replication and is an important part of the ultimate failure to eradicate the virus. Disclosed herein are methods for genetically enhancing the HIV-specific CTL response to allow long-term viral suppression or viral clearance. Human hematopoietic stem cells (HSCs) were genetically modified such that they differentiate into mature CTLs that will kill HIV infected cells. As disclosed herein, the functional effector cells are not human leukocyte antigen (HLA)-restricted. As disclosed herein, stem cells are transduced with non-HLA restricted chimeric antigen receptors (CARs) that allow the recognition of HIV or HIV-infected cells when expressed by a CTL. These CARs are hybrid molecules that contain an extracellular HIV recognition domain and an intracellular TCR-zeta signaling domain. The CTL response may be enhanced through the targeting of T cell inhibitory receptors. The methods and compositions disclosed herein may be used to engineer antiviral immunity and HIV-specific CTL responses in vivo. Also disclosed herein are methods and compositions for the treatment of chronic viral infections such as HIV.