Dilution of reacting species by build-up of helium ash and its effect on ignition in the ITER tokamak have been studied in a series of simulations with the one-dimensional BALDUR transport code. Thermal diffusivities, obtained from ITER scaling laws and with radial variations observed in JET, gave rg s= 2-4 sec. Refuelling of deuterium and tritium maintained constant electron density, while carbon recycling was 1009c and the helium ash recycling was varied from 1.0 to 0.5, Including MHD effects, specifically sawteeth and beta limits, we find that ignition can be sustained for 200 seconds with Rhmii um = 0.95. These simulations, the only non-zerodimensional, time-dependent simulations thus far made for ITER plasmas, emphasize that edge plasma conditions, MHD behavior, and helium particle transport are critical syner gistic issues for sustained ignition.