We study stochastic choice as the outcome of deliberate randomization. After first deriving a general representation of a stochastic choice function with such property, we proceed to characterize a model in which the agent has preferences over lotteries that belong to the Cautious Expected Utility class (Cerreia Vioglio et al., 2015), and the stochastic choice is the optimal mix among available options. This model links stochasticity of choice and the phenomenon of Certainty Bias, with both behaviors stemming from the same source: multiple utilities and caution. We show that this model is behaviorally distinct from models of Random Utility, as it typically violates the property of Regularity, shared by all of them.