The problem of a flame stabilized by a line source of fuel in the cellular regime, i.e., $L < 1$,where L is the Lewis number, is solved numerically. It is found that as L is decreased, transitions from stationary axisymmetric to stationary cellular to nonstationary cellular flames occur. The nonstationary cellular flames can exhibit both periodic and quasi-periodic dynamics. In particular, as L is decreased successive transitions from stationary axisymmetric solutions, to stationary four-cell solutions, to spinning four-cell solutions are computed. The spinning four-cell solutions are very slowly traveling waves that arise due to an infinite period, symmetry breaking bifurcation, in which the reflection symmetry of the stationary four-cell solution is broken. Near the transition point, the traveling wave solution branch is unstable and perturbations evolve to either a stationary five-cell or a nonstationary mixed-mode solution exhibiting apparently quasi-periodic dynamics. If L is further decreased beyond...