Peer review and rebuttal, with rich interactions and argumentative discussions in between, are naturally a good resource to mine arguments. However, few works study both of them simultaneously. In this paper, we introduce a new argument pair extraction (APE) task on peer review and rebuttal in order to study the contents, the structure and the connections between them. We prepare a challenging dataset that contains 4,764 fully annotated review-rebuttal passage pairs from an open review platform to facilitate the study of this task. To automatically detect argumentative propositions and extract argument pairs from this corpus, we cast it as the combination of a sequence labeling task and a text relation classification task. Thus, we propose a multitask learning framework based on hierarchical LSTM networks. Extensive experiments and analysis demonstrate the effectiveness of our multi-task framework, and also show the challenges of the new task as well as motivate future research directions.