Reviewing and comprehending key obligations, entitlements, and prohibitions in legal contracts can be a tedious task due to their length and domain-specificity. Furthermore, the key rights and duties requiring review vary for each contracting party. In this work, we propose a new task of party-specific extractive summarization for legal contracts to facilitate faster reviewing and improved comprehension of rights and duties. To facilitate this, we curate a dataset comprising of party-specific pairwise importance comparisons annotated by legal experts, covering ~293K sentence pairs that include obligations, entitlements, and prohibitions extracted from lease agreements. Using this dataset, we train a pairwise importance ranker and propose a pipeline-based extractive summarization system that generates a party-specific contract summary. We establish the need for incorporating domain-specific notions of importance during summarization by comparing our system against various baselines using both automatic and human evaluation methods.