Customer care is important for its role in relationship-building. This role has traditionally been performed by human customer agents, given the less mature feeling intelligence of AI. The emergence of interactive generative AI (GenAI) shows the potential for using AI for customer care in such emotionally charged interactions. Bridging practice and the academic literatures in marketing and computer science, this paper develops an AI-enabled customer care journey, beginning from accurate emotion recognition to empathetic response, emotional management support, and finally, the establishment of an emotional connection. Marketing requirements for each of the stages are derived from in-depth top manager interviews and a CMO survey. By juxtaposing these requirements against the current feeling capabilities of GenAI, the technological challenges that need to be tackled by engineers are highlighted. This paper wraps up with a set of marketing tenets for implementing and researching the caring machine. These marketing tenets encompass verifying emotion recognition accuracy using marketing emotion theories through multiple emotion signals and methods, utilizing prompt engineering to let customers reveal their thinking and feeling to enhance emotion understanding, employing “response engineering” for knowledge of customer preferences to personalize emotion management recommendation, and strategically deploying GenAI for emotional connection to simultaneously enhance customer emotional well-being and customer lifetime value.