Claim span identification (CSI) is an important step in fact-checking pipelines, aiming to identify text segments that contain a checkworthy claim or assertion in a social media post. Despite its importance to journalists and human fact-checkers, it remains a severely understudied problem, and the scarce research on this topic so far has only focused on English.Here we aim to bridge this gap by creating a novel dataset, X-CLAIM, consisting of 7K realworld claims collected from numerous social media platforms in five Indian languages and English. We report strong baselines with stateof-the-art encoder-only language models (e.g., XLM-R) and we demonstrate the benefits of training on multiple languages over alternative cross-lingual transfer methods such as zeroshot transfer, or training on translated data, from a high-resource language such as English. We evaluate generative large language models from the GPT series using prompting methods on the X-CLAIM dataset and we find that they underperform the smaller encoder-only language models for low-resource languages. 1 † Major part of this work was done during a research internship at MBZUAI.