Fe-Mg interdiffusion coefficients for (Mg,Fe)SiO3 perovskite have been measured at pressures of 22 to 26 gigapascals and temperatures between 1973 and 2273 kelvin. Perovskite Fe-Mg interdiffusion is as slow as Si self-diffusion and is orders of magnitude slower than Fe-Mg diffusion in other mantle minerals. Length scales over which chemical heterogeneities can homogenize, throughout the depth range of the lower mantle, are limited to a few meters even on time scales equivalent to the age of Earth. Heterogeneities can therefore only equilibrate chemically when they are stretched and thinned by intense deformation.