We study chemical reaction fronts described by the Kuramoto–Sivashinsky equation coupled to surface tension driven flow. We consider the front as a thin interface separating reacted from unreacted fluids inside a two-dimensional fluid layer. The top surface of the layer is open to the atmosphere. Fluid motion is caused by surface tension gradients across the reaction front. We use the equations describing Stokes flow to model the fluid motion inside the fluid layer. We apply a linear stability analysis to determine the stability of the steady front solutions. We find that initially unstable fronts can become stable due to fluid motion.