As an acid flows through porous rock, it etches the rock and so increases the permeability. This propagating reaction front suffers an instability, rather like the viscous fingering instability, in which the acid prefers to follow high-permeability channels which it has already etched. We have examined the linear stability, obtaining analytic results for small and large wavenumbers and for small variations of the permeability, and obtaining numerical results in other cases.