This paper presents a study of a novel summarization problem called contrastive opinion summarization (COS). Given two sets of positively and negatively opinionated sentences which are often the output of an existing opinion summarizer, COS aims to extract comparable sentences from each set of opinions and generate a comparative summary containing a set of contrastive sentence pairs. We formally formulate the problem as an optimization problem and propose two general methods for generating a comparative summary using the framework, both of which rely on measuring the content similarity and contrastive similarity of two sentences. We study several strategies to compute these two similarities. We also create a test data set for evaluating such a novel summarization problem. Experiment results on this test set show that the proposed methods are effective for generating comparative summaries of contradictory opinions.