The administration of a genetically engineered defective interfering virus (DIV) that interferes with HIV-1 replication has been proposed as a therapy for HIV-1 infection and AIDS. The proposed interfering virus, which is designed to superinfect HIV-1 infected cells, carries ribozymes that cleave conserved regions in HIV-1 RNA that code for the viral envelope protein. Thus DIV infection of HIV-1 infected cells should reduce or eliminate viral production by these cells. The success of this therapeutic strategy will depend both on the intercellular interaction of DIV and HIV-1, and on the overall dynamics of virus and T cells in the body. To study these dynamical issues, we have constructed a mathematical model of the interaction of HIV-1, DIV, and CD4+ cells in vivo. The results of both mathematical analysis and numerical simulation indicate that survival of the engineered DIV purely on a peripheral blood HIV-1 infection is unlikely. However, analytical results indicate that DIV might well survive on HIV-1 infected CD4+ cells in lymphoid organs such as lymph nodes and spleen, or on other HIV-1 infected cells in these organs.