Ambiguity in the ordinary language sense means that available information is open to multiple interpretations. We model this by assuming that individuals are unaware of some possibilities relevant to the outcome of their decisions and that multiple probabilities may arise over an individual's subjective state space depending on which of these possibilities are realized. We formalize a notion of coherent multiple priors and derive a representation result that with full awareness corresponds to the usual unique (Bayesian) prior but with less than full awareness generates multiple priors. When information is received with no change in awareness, each element of the set of priors is updated in the standard Bayesian fashion (that is, full Bayesian updating). An increase in awareness, however, leads to an expansion of the individual's subjective state and (in general) a contraction in the set of priors under consideration. Keywords ambiguity, unawareness, multiple priors. JEL Classification: D81 * We thank Adam Dominiak, Peter Klibanoff, Sujoy Mukerji, Klaus Nehring, and participants at RUD2019 and at the economics seminar at UGA. We are also especially grateful to the guest editor and two anonymous referees for their patience and perseverance in reviewing earlier versions and providing us with many useful comments and suggestions that have considerably improved the clarity of our exposition.