A sentence containing disjunction in the scope of a possibility modal, such as Angie is allowed to buy the car or the boat, gives rise to the FREE CHOICE inference that Angie can freely choose between the two. This inference poses a well-known puzzle, in that it is not predicted by a standard treatment of modals and disjunction (e.g., Kamp 1974). To complicate things further, FREE CHOICE tends to disappear under negation: Angie is not allowed to buy the car or the boat doesn’t merely convey the negation of free choice, but rather the stronger DUAL PROHIBITION reading that Angie cannot buy either one. There are two main approaches to the FREE CHOICE-DUAL PROHIBITION pattern in the literature. While they both capture the relevant data points, they make a testable, divergent prediction regarding the status of positive and negative sentences in a context in which Angie can only buy one of the two objects, e.g., the boat. In particular, the implicature- based approach (e.g., Fox 2007; Klinedinst 2007; Bar-Lev & Fox 2017) predicts that the positive sentence is true in such a context, but associated with a false implicature, while the negative sentence is predicted to be straightforwardly false. The alternative approach (e.g., Aloni 2018; Goldstein 2018; Willer 2017) predicts both the positive and negative sentences to be equally undefined. Investigating the contrast between these sentences in such a context, therefore, provides a clear way to address the debate between implicature and non-implicature accounts of FREE CHOICE. We present an experiment aiming to do just this, the results of which present a challenge for the implicature approach. We further discuss how the implicature approach could, in theory, be developed to account for our results, based on a recent proposal by Enguehard & Chemla (2018) on the distribution of implicatures.