The morphological stability of a mineralogically sharp and planar dissolution front separating rock A from rock B during reactive dissolution in a multicomponent system was examined using a linear stability analysis. In the absence of melt flow, the underlining cause for the instability is chemical diffusion in the melt. The destabilizing chemical diffusion gives rise to a new class of morphological instability in which the maximum growth rate of the perturbation corresponds to the minimum wavelength of the porous system that is on the order of a few grain sizes. On the geological outcrop scale a chemical diffusion induced unstable dissolution front separating two rock units would appear diffuse. The diffuse boundaries between the harzburgite and dunite observed in ophiolites may be a result of such dissolution instability. When chemical diffusion is stabilizing the wavelength of the instability is larger and sharp lithological boundary can be preserved.