The uptake of chatbots for customer service depends on the user experience. For such chatbots, user experience in particular concerns whether the user is provided relevant answers to their queries and the chatbot interaction brings them closer to resolving their problem. Dialogue data from interactions between users and chatbots represents a potentially valuable source of insight into user experience. However, there is a need for knowledge of how to make use of these data. Motivated by this, we present a framework for qualitative analysis of chatbot dialogues in the customer service domain. The framework has been developed across several studies involving two chatbots for customer service, in collaboration with the chatbot hosts. We present the framework and illustrate its application with insights from three case examples. Through the case findings, we show how the framework may provide insight into key drivers of user experience, including response relevance and dialogue helpfulness (Case 1), insight to drive chatbot improvement in practice (Case 2), and insight of theoretical and practical relevance for understanding chatbot user types and interaction patterns (Case 3). On the basis of the findings, we discuss the strengths and limitations of the framework, its theoretical and practical implications, and directions for future work.