The speed of the laminar flame in a degenerate carbon-oxygen white dwarf is too slow to produce a Type I supernova. We draw attention to the role of the Landau instability in wrinkling the flame front. This roughening of the front surface can cause an appreciable enhancement in the flame velocity. For typical presupernova conditions the density jump across the front is small. This implies the applicability of the “potential approximation” for describing the flow pattern and allows derivation of the Frankel equation for flame propagation. We report the results of our numerical experiments with this equation in a highly nonlinear regime. These calculations, coupled with analytic approximations allow us to determine the dependence of the fractal dimension of the front surface on the density jump across the front. Astrophysical implications of our results are discussed.