The interaction of a premixed stoichiometric methane-air flame with a two-dimensional counter-rotating vortex-pair is studied using a skeletal C-1 chemical mechanism. The focus is on the modification to flame structure and dynamic due to unsteady strain rate and curvature. Results demonstrate the overall contortion of the flame by the vortex pair, and the generation and entrainment of baroclinic vorticity. Observations at the positively curved cusp (convex towards the reactants) indicate modifications to flame structure due to diffusional focusing and defocusing of intermediates internal to the flame. The defocusing of the H atom is found to have the largest influence on the reduction of CH4 consumption and the retardation of reaction rates at the cusp. Vortex-pair centerline data suggest that the dame tends towards extinction due to its relative motion into the products. Increased temperature and products concentrations in the reaction zone tend to deplete H, while the scarcity of O-2 associated with a relative shift towards the products reduces the chain-branching rates, depleting O and OH. This scarcity of radicals reduces the overall consumption rate of fuel. leading the flame towards extinction.