The possibility of obtaining ignition in the Tokamak Fusion Test Reactor (TFTR) by means of very centrally peaked density profiles is examined. It is shown that local central alpha heating can be made to exceed local central energy losses (“central ignition”) under global conditions for which Q 1. Time-dependent one-dimensional transport simulations with a simplified transport model show that the normal global ignition requirements are substantially relaxed for plasmas with peaked density profiles. More realistic simulations with recently developed profile-consistent microinstability based models for electron and ion confinement show that TFTR may form a small centrally ignited region if peaked central density can be maintained.