Dialogue systems are usually categorized into two types, open-domain and task-oriented. The first one focuses on chatting with users and making them engage in the conversations, where selecting a proper topic to fit the dialogue context is essential for a successful dialogue. The other one focuses on a specific task instead of casual talks, e.g., finding a movie on Friday night, playing a song. These two directions have been studied separately due to their different purposes. However, how to smoothly transition from social chatting to task-oriented dialogues is important for triggering the business opportunities, and there is no any public data focusing on such scenarios. Hence, this paper focuses on investigating the conversations starting from open-domain social chatting and then gradually transitioning to task-oriented purposes, and releases a large-scale dataset with detailed annotations for encouraging this research direction. To achieve this goal, this paper proposes a framework to automatically generate many dialogues without human involvement, in which any powerful open-domain dialogue generation model can be easily leveraged. The human evaluation shows that our generated dialogue data has a natural flow at a reasonable quality, showing that our released data has a great potential of guiding future research directions and commercial activities. Furthermore, the released models allow researchers to automatically generate unlimited dialogues in the target scenarios, which can greatly benefit semi-supervised and unsupervised approaches.