Highly active antiretroviral therapy (ART) has successfully turned Human immunodeficiency virus type 1 (HIV-1) from a deadly pathogen into a manageable chronic infection. ART is a lifelong therapy which is both expensive and toxic, and HIV can become resistant to it. An alternative to lifelong ART is gene therapy that targets the CCR5 co-receptor and creates a population of genetically modified host cells that are less susceptible to viral infection. With generic mathematical models we show that gene therapy that only targets the CCR5 co-receptor fails to suppress HIV-1 (which is in agreement with current data). We predict that the same gene therapy can be markedly improved if it is combined with a suicide gene that is only expressed upon HIV-1 infection.