The origin and timing of the diversification of modern birds remains controversial, primarily because phylogenetic relationships are incompletely resolved and uncertainty persists in molecular estimates of lineage ages. Here, we present a species tree for the major palaeognath lineages using 27 nuclear genes and 27 archaic retroposon insertions. We show that rheas are sister to the kiwis, emu and cassowaries, and confirm ratite paraphyly because tinamous are sister to moas. Divergence dating using 10 genes with broader taxon sampling, including emu, cassowary, ostrich, five kiwis, two rheas, three tinamous, three extinct moas and 15 neognath lineages, suggests that three vicariant events and possibly two dispersals are required to explain their historical biogeography. The age of crown group birds was estimated at 131 Ma (95% highest posterior density 122-138 Ma), similar to previous molecular estimates. Problems associated with gene tree discordance and incomplete lineage sorting in birds will require much larger gene sets to increase species tree accuracy and improve error in divergence times. The relatively rapid branching within neoaves pre-dates the extinction of dinosaurs, suggesting that the genesis of the radiation within this diverse clade of birds was not in response to the Cretaceous-Paleogene extinction event.