We study the pattern formation in a chemical two-layer system, placed in a Hele-Shaw cell. The upper layer is an organic solvent in which a carboxylic acid is dissolved. The lower layer consists of water containing an inorganic base. We report on a novel instability type which is driven by an exothermic neutralization reaction in vicinity to the interface. This instability combines plume and finger regimes and gives rise to a self-sustained dynamics.