Automated Graphical User Interface (GUI) testing plays a crucial role in ensuring app quality, especially as mobile applications have become an integral part of our daily lives. Despite the growing popularity of learning-based techniques in automated GUI testing due to their ability to generate human-like interactions, they still suffer from several limitations, such as low testing coverage, inadequate generalization capabilities, and heavy reliance on training data. Inspired by the success of Large Language Models (LLMs) like ChatGPT in natural language understanding and question answering, we formulate the mobile GUI testing problem as a Q&A task. We propose GPTDroid, asking LLM to chat with the mobile apps by passing the GUI page information to LLM to elicit testing scripts, and executing them to keep passing the app feedback to LLM, iterating the whole process. Within this framework, we have also introduced a functionality-aware memory prompting mechanism that equips the LLM with the ability to retain testing knowledge of the whole process and conduct long-term, functionality-based reasoning to guide exploration. We evaluate it on 93 apps from Google Play and demonstrate that it outperforms the best baseline by 32% in activity coverage, and detects 31% more bugs at a faster rate. Moreover, GPTDroid identify 53 new bugs on Google Play, of which 35 have been confirmed and fixed.