The quantitative contribution of the thymus to the maintenance of peripheral populations of naive T cells is poorly understood. Several new lines of evidence indicate that thymic activity continues into adulthood, albeit at lower levels than in early life, and that this is important for a range of lymphopenic disorders. A measure of thymic activity that is often used is the quantification of T-cell receptor excision circles (TRECs). It has been shown that TREC levels decline after infection with HIV-1 and that they recover to above normal levels after antiretroviral treatment. The reasons for the latter observation are unknown. Here we quantitatively explore different possible causes for supranormal levels of TREC per cell and show that the small total number of cells involved in reconstituting the TREC+ T-cell pool of HIV-1-infected patients suffices to explain the observation. Even the expected small thymic outputs into a strongly depleted naive T-cell peripheral pool lead to a slow transient of elevated levels of TREC per cell. The main biological lesson from our quantitative modeling approach is that middle-aged human thymi continue to produce naive T cells and that this production can be demonstrated by tracking the increase of total TREC numbers (rather than the TREC content).