In community-based software development, developers frequently rely on live-chatting to discuss emergent bugs/errors they encounter in daily development tasks. However, it remains a challenging task to accurately record such knowledge due to the noisy nature of interleaved dialogs in live chat data. In this paper, we first formulate the task of identifying and synthesizing bug reports from community live chats, and propose a novel approach, named BugListener, to address the challenges. Specifically, BugListener automates three sub-tasks: 1) Disentangle the dialogs from massive chat logs by using a Feed-Forward neural network; 2) Identify the bug-report dialogs from separated dialogs by modeling the original dialog to the graph-structured dialog and leveraging the graph neural network to learn the contextual information; 3) Synthesize the bug reports by utilizing the TextCNN model and Transfer Learning network to classify the sentences into three groups: observed behaviors (OB), expected behaviors (EB), and steps to reproduce the bug (SR). BugListener is evaluated on six open source projects. The results show that: for bug report identification, BugListener achieves the average F1 of 74.21%, improving the best baseline by 10.37%; and for bug report synthesis task, BugListener could classify the OB, EB, and SR sentences with the F1 of 67.37%, 87.14%, and 65.03%, improving the best baselines by 7.21%, 7.38%, 5.30%, respectively. A human evaluation also confirms the effectiveness of BugListener in generating relevant and accurate bug reports. These demonstrate the significant potential of applying BugListener in community-based software development, for promoting bug discovery and quality improvement.