Neither essential chance nor contingent ignorance chance (neither indeterminacy nor uncertainty), the form of chance underlying the probabilistic character of quantum physics, needs to be better characterized.In this article we develop the intermediate concept of a chance of necessary ignorance. A randomness imposed by a limit of knowledge, on a par with the standard randomness of ignorance, except that here the limit is in principle insurmountable, unlike those encountered, for example, in classical statistical physics.