In this work, we take a step towards understanding and defending against spying browser extensions. These are extensions repurposed to capture online activities of a user and communicate the collected sensitive information to a third-party domain. We conduct an empirical study of such extensions on the Chrome Web Store. First, we present an in-depth analysis of the spying behavior of these extensions. We observe that these extensions steal a variety of sensitive user information, such as the complete browsing history (e.g., the sequence of web traversals), online social network (OSN) access tokens, IP address, and geolocation. Second, we investigate the potential for automatically detecting spying extensions by applying machine learning schemes. We show that using a Recurrent Neural Network (RNN), the sequence of browser API calls made by an extension can be a robust feature, outperforming hand-crafted features (used in prior work on malicious extensions) to detect spying extensions. Our RNN based detection scheme achieves a high precision (90.02%) and recall (93.31%) in detecting spying extensions.