Primates, consisting of apes, monkeys, tarsiers, and lemurs, are among the most charismatic and well-studied animals on Earth, yet there is no taxonomically complete molecular timetree for the group. Combining the latest large-scale genomic primate phylogeny of 205 recognized species with the 400-species literature consensus tree available from TimeTree.org yields a phylogeny of just 405 primates, with 50 species still missing despite having molecular sequence data in the NCBI GenBank. In this study, we assemble a timetree of 455 primates, incorporating every species for which molecular data are available. We use a synthetic approach consisting of a literature review for published timetrees, de novo dating of untimed trees, and assembly of timetrees from novel alignments. The resulting near-complete molecular timetree of primates allows testing of two long-standing alternate hypotheses for the origins of primate biodiversity: whether species richness arises at a constant rate, in which case older clades have more species, or whether some clades exhibit faster rates of speciation than others, in which case, these fast clades would be more species-rich. Consistent with other large-scale macroevolutionary analyses, we found that the speciation rate is similar across the primate tree of life, albeit with some variation in smaller clades.