Mounting evidence indicates that the Earth's mantle is chemically heterogeneous. To understand the forms that convection might take in such a mantle, I have conducted laboratory experiments on thermochemical convection in a fluid with stratified density and viscosity. For intermediate density contrasts, a ‘doming’ regime of convection is observed, in which hot domes oscillate vertically through the whole layer while thin tubular plumes rise from their upper surfaces. These plumes could be responsible for the ‘hot spots’ and the domes themselves for the ‘superwells’ observed at the Earth's surface. In the Earth's mantle, the doming regime should occur for density contrasts less than about 1%. Moreover, quantitative scaling laws derived from the experiments show that the mantle might have evolved from strictly stratified convection 4 Gyr ago to doming today. Thermochemical convection can thus reconcile the survival of geochemically distinct reservoirs with the small amplitude of present-day density heterogeneities inferred from seismology and mineral physics.