At present, tropical arid biomes house less woody plant species diversity than tropical moist biomes, which could be due to lower rates of evolutionary diversification in the recent or distant past. Here, we study the evolutionary diversification of Petalidium (Acanthaceae), a genus of 36 species of woody shrubs found in the Namib Desert of southwest Africa, and surrounding areas. We generated a new, nearly fully sampled and temporally calibrated phylogeny for Petalidium using RADseq SNP data and secondary calibrations. We then investigated variation in net diversification rate across the phylogeny, the ancestral climatic niche of lineages and the link between the two. We find that arid climatic conditions are linked with increased rates of net species diversification in the genus. Despite its great age, the Namib Desert clearly hosts young plant radiations. This apparent contradiction can be explained by a scenario of high evolutionary turnover, in this case potentially caused by alternating hyper-arid and relatively mesic phases. Hyper-arid phases could result in high plant mortality and extinction of species, leading to ecological opportunity and diversification during mesic phases. Taken together, our results contribute to a growing body of literature that shows evidence for elevated rates of plant diversification in the Quaternary in arid biomes across the globe. Keywords: Namib Desert, arid biomes, Acanthaceae, plant diversification, RAD sequencing.