We present an experimental investigation of a novel low Reynolds number shear flow instability triggered by a chemical reaction. An acid-base reaction taking place at the interface between a Newtonian fluid and Carbopol-940 solution leads to a strong viscosity stratification, which locally destabilizes the flow. Our experimental observations are made in the context of a miscible displacement flow, for which the flow instability promotes local mixing and subsequently improves the displacement efficiency. The experimental study is complemented by a simplified normal mode analysis to shed light on the origin of the instability