THE Tibetan plateau has had a central role in the development of recent models for the mechanics of mountain belts1,2 and Cenozoic global climate change3. The present elevation and extensional deformation of the plateau probably result from uplift owing to convective thinning of the underlying lithospheric mantle1,2. An age for the uplift would provide a valuable constraint on these models; but because recently proposed indicators of uplift are all climate-dependent, they are equivocal, possibly reflecting global cooling rather than regional uplift4. Here we present new geochemical data on post-mid-Miocene lavas from the plateau, which show that the lavas were derived from the lithospheric mantle. Simple thermal arguments indicate that the generation of such magmas also necessitates thinning of the lithospheric mantle. Thus volcanism is coincident with uplift, providing a climate-independent means of dating the onset of uplift. Dating by the laser Ar-40/Ar-39 technique places the beginning of this volcanism, and therefore the time of uplift of the Tibetan plateau, at 13 Myr ago.