In certain mixtures : of fuel and oxidizer, propagating flame fronts may exhibit both stable and unstable cellular structures : Such flames represent spatially extended chemical systems, with coupling from diffusion of heat and reactants. A new algorithm is proposed that allows the stabilization and tracking of a steady, two-cell front through a bifurcation sequence that eventually leads to chaotic behavior. Periodic modes of the front can also be stabilized and tracked. The system is stabilized by monitoring one experimentally accessible variable and perturbing one boundary condition. No knowledge of the detailed dynamics of the system (i.e., the underlying governing equations) is required to implement the tracking method. The algorithm automatically provides information about the locations of the unstable steady states and periodic orbits and the magnitudes of the associated eigenvalues aria Floquet multipliers.