We offer a theory of polarization as an optimal response to ambiguity. Suppose two individuals have different priors and individual A's beliefs first-order stochastically dominate individual B's. The individuals observe a common signal. Their beliefs exhibit polarization if individual A's posterior dominates her prior and individual B's prior dominates her posterior. We show a sense in which polarization is impossible under Bayesian updating and after the observation of extreme signals. However, we also show that polarization after observing an intermediate signal can arise from the efforts of ambiguity averse individuals to implement their optimal prediction strategies through dynamically consistent updating. When ambiguity averse individuals' beliefs are sufficiently close to opposite extremes, observing a neutral signal always leads to polarization. Under additional assumptions, we show that updating follows a threshold rule, allowing a more precise characterization of the conditions for polarization.