Having a large number of sufficiently abundant T cell clones is important for adequate protection against diseases. However, as shown in this paper and elsewhere, between young adulthood and >70 y of age the effective clonal diversity of naive CD4/CD8 T cells found in human blood declines by a factor of >10. (Effective clonal diversity accounts for both the number and the abundance of T cell clones.) The causes of this observation are incompletely understood. A previous study proposed that it might result from the emergence of certain rare, replication-enhancing mutations in T cells. In this paper, we propose an even simpler explanation: that it results from the loss of T cells that have attained replicative senescence (i.e., the Hayflick limit). Stochastic numerical simulations of naive T cell population dynamics, based on experimental parameters, show that the rate of homeostatic T cell proliferation increases after the age of ∼60 y because naive T cells collectively approach replicative senescence. This leads to a sharp decline of effective clonal diversity after ∼70 y, in agreement with empirical data. A mathematical analysis predicts that, without an increase in the naive T cell proliferation rate, this decline will occur >50 yr later than empirically observed. These results are consistent with a model in which exhaustion of the proliferative capacity of naive T cells causes a sharp decline of their effective clonal diversity and imply that therapeutic potentiation of thymopoiesis might either prevent or reverse this outcome.