The energy and species conservation equations are considered in spherical geometry with Arrhenius kinetics. The model is thermal-diffusional (i.e. no fluid mechanical effects are considered). Asymptotic analysis is carried out and stability analysis of the two solutions demonstrated is carried out. The effect of Lewis number on stability is examined showing the main conclusion that flame balls can only exist for sufficiently small Lewis number. However sufficiently large solutions are always unstable to three dimensional perturbations for any Lewis number.