Suppression of HIV replication by antiretroviral therapy (ART) or host immunity can prevent AIDS but not other HIV-associated conditions including neurocognitive impairment (HIV-NCI). Pathogenesis in HIV-suppressed individuals has been attributed to reservoirs of latent-inducible virus in resting CD4+ T cells. Macrophages are persistently infected with HIV but their role as HIV reservoirs in vivo has not been fully explored. Here we show that infection of conventional mice with chimeric HIV, EcoHIV, reproduces physiological conditions for development of disease in people on ART including immunocompetence, stable suppression of HIV replication, persistence of integrated, replication-competent HIV in T cells and macrophages, and manifestation of learning and memory deficits in behavioral tests, termed here murine HIV-NCI. EcoHIV established latent reservoirs in CD4+ T lymphocytes in chronically-infected mice but could be induced by epigenetic modulators ex vivo and in mice. In contrast, macrophages expressed EcoHIV constitutively in mice for up to 16 months; murine leukemia virus (MLV), the donor of gp80 envelope in EcoHIV, did not infect macrophages. Both EcoHIV and MLV were found in brain tissue of infected mice but only EcoHIV induced NCI. Murine HIV-NCI was prevented by antiretroviral prophylaxis but once established neither persistent EcoHIV infection in mice nor NCI could be reversed by long-acting antiretroviral therapy. EcoHIV-infected, athymic mice were more permissive to virus replication in macrophages than were wild-type mice, suffered cognitive dysfunction, as well as increased numbers of monocytes and macrophages infiltrating the brain. Our results suggest an important role of HIV expressing macrophages in HIV neuropathogenesis in hosts with suppressed HIV replication. Antiretroviral therapy (ART) transformed HIV infection from a death sentence to a chronic, largely manageable condition, with near preservation of immune systems and extended life expectancies in infected people. Despite effective ART, roughly half of HIV-infected people suffer problems in learning and memory that can impair day to day activities. In addition, HIV persists in largely silent states during ART, but it can be reactivated and produce infectious, possibly pathogenic virus. We addressed these two issues by infecting mice with a genetically engineered HIV that infects rodents instead of human beings. Unlike infected people we find that infected mice maintain good immune responses to HIV that appear to act like ART to keep virus levels low and allow mice to resist other complications. Like infected people, HIV-infected mice are subject to learning and memory problems; they carry silenced HIV long-term in T lymphocytes but we found that macrophages, infected in both humans and mice, continue to produce HIV in mice indicating that additional means may be needed to control HIV-infected macrophages. Moreover, in mice lacking T lymphocytes HIV infection of macrophages is sufficient to drive dysfunction in learning and memory. Like in people living with HIV, antiretroviral therapy in chronically-infected mice is ineffective against existing HIV infection and cognitive disease. Controlling this infection and brain disease may require tools tailored to actively expressed virus.