The complexities of chats, such as the stylized contents specific to source segments and dialogue consistency, pose significant challenges for machine translation. Recognizing the need for a precise evaluation metric to address the issues associated with chat translation, this study introduces Multidimensional Quality Metrics for Chat Translation (MQM-Chat), which encompasses seven error types, including three specifically designed for chat translations: ambiguity and disambiguation, buzzword or loanword issues, and dialogue inconsistency. In this study, human annotations were applied to the translations of chat data generated by five translation models. Based on the error distribution of MQM-Chat and the performance of relabeling errors into chat-specific types, we concluded that MQM-Chat effectively classified the errors while highlighting chat-specific issues explicitly. The results demonstrate that MQM-Chat can qualify both the lexical accuracy and semantical accuracy of translation models in chat translation tasks.