We analyse the linear stability of a reactive plane Poiseuille flow, where a reactant fluid A overlies another reactant B in a layered fashion within a two-dimensional channel. Both reactants are miscible and have the same viscosity, while upon reaction, they produce either a less or more-viscous product fluid C. The reaction kinetics is of simple A+B→C type, and the production of C occurs across the initial contact line of reactants A and B in a mixed zone of small and finite width. All three fluids have the same density. We demonstrate the effects of various controlling parameters such as the log-mobility ratio, Damköhler number, Schmidt number, Reynolds number, position and thicknesses of the reactive zone on the stability characteristics. We show that a tiny viscosity stratification by the reaction destabilizes the flow at a moderate (10-1000) and even at low Reynolds numbers (0.01-1). The maximum growth occurs for shorter waves than for the Tollmien-Schlichting eigenmode, and the ranges of unstable wavenumbers are wider than that known for non-reactive channel flow systems. In most cases, the instability occurs due to the overlap of the critical layer with the viscosity-stratified layer. Surprisingly for some parameters, it is observed that the reaction can make σM decrease with increasing Reynolds number. © 2023 The Author(s).