Recent work has addressed the problem of detecting relevant claims for a given controversial topic. We introduce the complementary task of Claim Stance Classification, along with the first benchmark dataset for this task. We decompose this problem into: (a) open-domain target identification for topic and claim (b) sentiment classification for each target, and (c) open-domain contrast detection between the topic and the claim targets. Manual annotation of the dataset confirms the applicability and validity of our model. We describe an implementation of our model, focusing on a novel algorithm for contrast detection. Our approach achieves promising results, and is shown to outperform several baselines, which represent the common practice of applying a single, monolithic classifier for stance classification.