HIV evolves rapidly within individuals, allowing phylogenetic studies to infer histories of viral lineages on short time scales. Latent HIV sequences are an exception to this rapid evolution, as their transcriptional inactivity leads to negligible mutation rates compared with non-latent HIV lineages. This difference in mutation rates generates potential information about the times at which sequences entered the latent reservoir, providing insight into the dynamics of the latent reservoir. A Bayesian phylogenetic method is developed to infer integration times of latent HIV sequences. The method uses informative priors to incorporate biologically sensible bounds on inferences (such as requiring sequences to become latent before being sampled) that many existing methods lack. A new simulation method is also developed, based on widely used epidemiological models of within-host viral dynamics, and applied to evaluate the new method-showing that point estimates and credible intervals are often more accurate than existing methods. Accurate estimates of latent integration dates are crucial in relating integration times to key events during HIV infection, such as treatment initiation. The method is applied to publicly available sequence data from four HIV patients, providing new insights regarding the temporal pattern of latent integration.