A calibrated theory-based tokamak transport model is applied to International Thermonuclear Experimental Reactor (ITER) ignition studies. The reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn can be achieved provided that impurity control makes radiative losses sufficiently small. The ignition probabilities of both ITER EDA and concept design activity parameters are investigated. These results suggest that a high-energy auxiliary heating power significantly <100 MW should heat ITER EDA to ignition.