The Cracidae (curassows, guans, and chachalacas) include some of the most spectacular and endangered Neotropical bird species. They lack a comprehensive phylogenetic hypothesis, hence their geographic origin and the history of their diversification remain unclear. We present a species-level phylogeny of Cracidae inferred from a matrix of 430 ultraconserved elements (UCEs; at least one species sampled per genus) and eight more variable loci (introns and mtDNA; all available species). We use this phylogeny along with probabilistic biogeographic modeling to test whether Gondwanan vicariance, ancient dispersal to South America, ancient dispersal from South America, or massive global cooling isolated cracids in the Neotropics. Contrary to previous estimates that extant cracids diversified in the Cretaceous, our fossil-calibrated divergence time estimates instead support that crown Cracidae originated in the late Miocene. Species-rich genera Crax, Penelope, and Ortalis began diversifying as recently as 3 Mya. Biogeographic reconstructions indicate that modern cracids originated in Mesoamerica and were isolated from a widespread Laurasian ancestor, consistent with the massive global cooling hypothesis. Current South American diversity is the result of multiple colonization events following uplift of the Panamanian Isthmus, coupled with rapid diversification and evolution of secondary sympatry. Of the four major cracid lineages (curassows, chachalacas, typical guans, horned guan), the only lineage that has failed to colonize and diversify South America is the unique horned guan (Oreophasis derbianus), which is sister to curassows and chachalacas rather than typical guans.