In this paper we study identification and inference of preference parameters in a single-agent, static, discrete choice model where the decision maker may face attentional limits precluding her to exhaustively process information about the payoffs of the available alternatives. By leveraging on the notion of one-player Bayesian Correlated Equilibrium in Bergemann and Morris (2016), we provide a tractable characterisation of the sharp identified set and discuss inference under minimal assumptions on the amount of information processed by the decision maker and under no assumptions on the rule with which the decision maker resolves ties. Simulations reveal that the obtained bounds on the preference parameters can be tight in several settings of empirical interest.