Although antiretroviral drug therapy suppresses human immunodeficiency virus-type 1 (HIV-1) to undetectable levels in the blood of treated individuals, reservoirs of replication competent HIV-1 endure. Upon cessation of antiretroviral therapy, the reservoir usually allows outgrowth of virus and approaches to targeting the reservoir have had limited success. Ongoing cycles of viral replication in regions with low drug penetration contribute to this persistence. Here, we use a mathematical model to illustrate a new approach to eliminating the part of the reservoir attributable to persistent replication in drug sanctuaries. Reducing the residency time of CD4 T cells in drug sanctuaries renders ongoing replication unsustainable in those sanctuaries. We hypothesize that, in combination with antiretroviral drugs, a strategy to orchestrate CD4 T cell trafficking could contribute to a functional cure for HIV-1 infection.