It is becoming increasingly easier for researchers and practitioners to collect eye tracking data during online preference measurement tasks. We develop a dynamic discrete choice model of information search and choice under bounded rationality, that we calibrate using a combination of eye-tracking and choice data. Our model extends the directed cognition model of Gabaix et al. (2006) by capturing fatigue, proximity effects, and imperfect memory encoding and by estimating individual-level parameters and partworths within a likelihood-based, hierarchical Bayesian framework. We show that modeling eye movements as the outcome of forward-looking utility maximization improves out-of-sample predictions, enables researchers and practitioners to use shorter questionnaires, and allows better discrimination between attributes.