The Brazilian Cerrado is the most species-rich tropical savanna in the world. Within this biome, the Campos Rupestres ('rocky savannas') constitute a poorly studied and highly threatened ecosystem. To better understand how plants characteristic of this vegetation have evolved and come to occupy the now widely-separated patches of rocky formations in eastern Brazil, we reconstruct the biogeographical history of the rare orchid genus Hoffmannseggella. We apply parsimony and Bayesian methods to infer the phylogenetic relationships among 40 out of the 41 described species. Absolute divergence times are calculated under penalized likelihood and compared with estimates from a Bayesian relaxed clock. Ancestral ranges are inferred for all nodes of the phylogeny using Fitch optimization and statistical dispersal vicariance analysis. In all analyses, phylogenetic uncertainty is taken into account by the independent analysis of a large tree sample. The results obtained indicate that Hoffmannseggella underwent rapid radiation around the Middle/Late Miocene (approximately 1114 Mya). The region corresponding today to southern Minas Gerais acted as amain source area for several independent range expansions north- and eastwards via episodic corridors. These results provide independent evidence that climate cooling following the Middle Miocene Climatic Optimum (approximately 15 Mya) led to important vegetational shifts in eastern Brazil, causing an increase in the dominance of open versus closed habitats. Polyploidy following secondary contact of previously isolated populations may have been responsible for the formation of many species, as demonstrated by the high ploidy levels reported in the genus.