We present a preference foundation for Chance Theory (CT), a model of decision making under uncertainty where the evaluation of an act depends distinctively on its lowest outcome. This outcome is evaluated with the riskless value function u and the potential increments over it are evaluated by subjective expected utility with a risky utility function u. In contrast to earlier approaches with models that aimed at separating riskless and risky utility, CT does not violate basic rationality principles like first-order stochastic dominance or transitivity. Decision makers with CT-preferences always prefer the expected value of a lottery to the latter, so they are weakly risk averse. Besides explaining behavioral irregularities like the expected utility paradoxes of Allais and Rabin, CT also separates risk attitude in the strong sense from attitude towards wealth. Risk attitude is completely determined by the curvature of vuand is independent of the value function v. Conversely, attitude towards wealth is reflected solely through the curvature of v without imposing constraints on u.