In recent years, intelligent chatbots have been widely used in the field of customer service. One of the key challenges for chatbots to maintain fluent dialogues with customers is how to respond at the appropriate time. However, most of the state-of-the-art chatbots follow the turn-by-turn interaction scheme. Such chatbots respond after each time when a customer sends an utterance, which in some cases leads to inappropriate responses and misleads the process of the dialogues. In this paper, we propose a multi-turn response triggering model (MRTM) to address this problem. MRTM is learned from large-scale human-human dialogues between the customers and the agents with a self-supervised learning scheme. It leverages the semantic matching relationships between the context and the response to train a semantic matching model and obtains the weights of the co-occurring utterances in the context through an asymmetrical self-attention mechanism. The weights are then used to determine whether the given context should be responded to. We conduct extensive experiments on two dialogue datasets collected from the real-world online customer service systems. Results show that MRTM outperforms the baselines by a large margin. Furthermore, we incorporate MRTM into DiDi’s customer service chatbot. Based on the ability to identify the appropriate time to respond, the chatbot can incrementally aggregate the information across multiple utterances and make more intelligent responses at the appropriate time.