Laboratory experiments were performed to study the influence of density and viscosity layering on the formation and stability of plumes. Viscosity ratios ranged from 0.1 to 6400 for buoyancy ratios between 0.3 and 20, and Rayleigh numbers between 10^5 and 2x10^8. The presence of a chemically stratified boundary layer generates long-lived thermochemical plumes. These plumes first develop from the interface as classical thermal boundary layer instabilities. As they rise, they entrain by viscous coupling a thin film of the other layer and locally deform the interface into cusps. The interfacial topography and the entrainment act to further anchor the plumes, which persist until the chemical stratification disappears through entrainment, even for Rayleigh numbers around 10^8. The pattern of thermochemical plumes remains the same during an experiment, drifting only slowly through the tank. Scaled to an Earth's mantle without plate tectonics, our results show that: (1) thermochemical plumes are expected to exist in the mantle, (2) they could easily survive hundreds of millions of years, depending on the size and magnitude of the chemical heterogeneity on which they are anchored, and (3) their drift velocity would be at most 1-2 mm/yr. They would therefore produce long-lived and relatively fixed hotspots on the lithosphere. However, the thermochemical plumes would follow any large scale motion imposed on the chemical layer. Therefore, the chemical heterogeneity acts more as a ‘floating anchor' than as an absolute one.