Surface tension driven convection affects the propagation of chemical reaction fronts in liquids. The changes in surface tension across the front generate this type of convection. The resulting fluid motion increases the speed and changes the shape of fronts as observed in the iodate-arsenous acid reaction. We calculate these effects using a thin front approximation, where the reaction front is modeled by an abrupt discontinuity between reacted and unreacted substances. We analyze the propagation of reaction fronts of small curvature. In this case the front propagation equation becomes the deterministic Kardar-Parisi-Zhang (KPZ) equation with the addition of fluid flow. These results are compared to calculations based on a set of reaction-diffusion-convection equations.