Pronouns are often dropped in Chinese sentences, and this happens more frequently in conversational genres as their referents can be easily understood from context. Recovering dropped pronouns is essential to applications such as Information Extraction where the referents of these dropped pronouns need to be resolved, or Machine Translation when Chinese is the source language. In this work, we present a novel end-to-end neural network model to recover dropped pronouns in conversational data. Our model is based on a structured attention mechanism that models the referents of dropped pronouns utilizing both sentence-level and word-level information. Results on three different conversational genres show that our approach achieves a significant improvement over the current state of the art.