This paper presents a theory to explain the development of immunodeficiency disease after a long and variable incubation period of infection with HIV-1. Two assumptions are central to the theory: (1) mutation via reverse transcription during viral replication can generate viral strains resistant to neutralization by antibodies specific to earlier mutants in a particular host; (2) the virus can kill the CD4-positive lymphocytes that play a role in mounting an immunological attack directed at the virus. The theory is examined via the development of a mathematical model which reveals that an increasing number of antigenically distinct viral strains may overwhelm the immune system of the host. As the viral diversity increases beyond a certain level the immune system is unable to suppress the population growth of all the strains simultaneously. The intuitive explanation of this pattern of model behaviour lies in the assumption that each virus can kill CD4-positive lymphocytes that are specific to any of the viral strains, but each lymphocyte only directs immunological attack against a single viral strain. The model captures several observed features of the interaction between HIV-1 and the human immune system: (1) an early peak in viraemia (primary HIV-1 infection) following infection; (2) a long and variable incubation period with low viral abundance for much of the period; (3) an increase of viral density in the final phase of infection as the failing immune system fails to control viral population growth (the appearance of the disease AIDS); (4) coevolution and coexistence of many viral mutants in one infected person, and (5) a positive correlation between the presence of high replicative viral strains and the rate of progression to disease (AIDS).