Dual approaches have proved their value in many areas of economic analysis. Until recently, however, they have been virtually ignored in the analysis of choice under uncertainty. In this paper, we present a dual formulation of choice under uncertainty based on a few simple assumptions about preferences, namely, continuity, monotonicity and convexity of preference sets. Particular emphasis is given to showing that the additive separability restriction, key to expected-utility theory, on preferences can be dropped with little loss of analytic power for a broad class of choice problems.