Local community detection (or local clustering) is of fundamental importance in large network analysis. Random walk based methods have been routinely used in this task. Most existing random walk methods are based on the single-walker model. However, without any guidance, a single-walker may not be adequate to effectively capture the local cluster. In this paper, we study a multi-walker chain (MWC) model, which allows multiple walkers to explore the network. Each walker is influenced (or pulled back) by all other walkers when deciding the next steps. This helps the walkers to stay as a group and within the cluster. We introduce two measures based on the mean and standard deviation of the visiting probabilities of the walkers. These measures not only can accurately identify the local cluster, but also help detect the cluster center and boundary, which cannot be achieved by the existing single-walker methods. We provide rigorous theoretical foundation for MWC, and devise efficient algorithms to compute it. Extensive experimental results on a variety of real-world networks demonstrate that MWC outperforms the state-of-the-art local community detection methods by a large margin.