Converging evidence suggests that we make decisions by comparing the value of the options in front of us, but how are these values represented in the brain? Many models assume that the representational geometry of value is linear, and this shape could be important for generating rational economic decisions. However, in part due to historical focus on noisy single neurons, rather than neural populations, the linearity hypothesis has not been rigorously tested. Here, we examined the representational geometry of value in populations of neurons recorded in the ventromedial prefrontal cortex (vmPFC), a part of the prefrontal cortex closely linked to economic decision-making. Monkeys performed a “menu search” task in which they chose between a set of reward cues associated with different volumes of juice. Although the average neuronal response to offer values was essentially linear, at the population level, multiple converging analyses suggested that offer values were encoded along a curved manifold in vmPFC. The curvilinear geometry predicted a specific violation of one of the axioms of rational decision-making, which posits that the preference between high-value options should not depend on adding irrelevant, low-value alternatives to the set. Instead, when the representation of values is curved, the upper bound on the accuracy of decoding high-value offers changes systematically with the value of the worst option in the set. Critically, monkeys exhibited exactly the paradoxical pattern of irrational choices predicted by the curvilinear manifold: the worse the irrelevant offer was, the more likely they were to confuse two good options. Together, these results suggest that neural representation of values may not be linear, as is generally assumed, but instead traces a curvilinear manifold, at least in vmPFC. This nonlinearity could be one cause of the systematic patterns of irrational economic decisions that appear in humans and other animals.