A central but little-tested prediction of "escape and radiation" coevolution is that colonization of novel, chemically defended host plant clades accelerates insect herbivore diversification. That theory, in turn, exemplifies one side of a broader debate about the relative influence on clade dynamics of intrinsic (biotic) vs. extrinsic (physical-environmental) forces. Here, we use a fossil-calibrated molecular chronogram to compare the effects of a major biotic factor (repeated shift to a chemically divergent host plant clade) and a major abiotic factor (global climate change) on the macroevolutionary dynamics of a large Cenozoic radiation of phytophagous insects, the leaf-mining fly genus Phytomyza (Diptera: Agromyzidae). We find one of the first statistically supported examples of consistently elevated net diversification accompanying shift to new plant clades. In contrast, we detect no significant direct effect on diversification of major global climate events in the early and late Oligocene. The broader paleoclimatic context strongly suggests, however, that climate change has at times had a strong indirect influence through its effect on the biotic environment. Repeated rapid Miocene radiation of these flies on temperate herbaceous asterids closely corresponds to the dramatic, climate-driven expansion of seasonal, open habitats.