X-rays are commonly performed imaging tests that use small amounts of radiation to produce pictures of the organs, tissues, and bones of the body. X-rays of the chest are used to detect abnormalities or diseases of the airways, blood vessels, bones, heart, and lungs. In this work we present a stochastic attention-based model that is capable of learning what regions within a chest X-ray scan should be visually explored in order to conclude that the scan contains a specific radiological abnormality. The proposed model is a recurrent neural network (RNN) that learns to sequentially sample the entire X-ray and focus only on informative areas that are likely to contain the relevant information. We report on experiments carried out with more than $100,000$ X-rays containing enlarged hearts or medical devices. The model has been trained using reinforcement learning methods to learn task-specific policies.