Despite growing interest in exploring the application of chatbots in language education, studies on the process of chatbot-assisted language learning are scant. This qualitative study uses activity theory to understand how English as a foreign language students engage with a chatbot, Argumate, when composing argumentative essays. Five Chinese undergraduate students performed an argumentative writing task with the assistance of Argumate. Screen recordings capturing the students' writing processes, chat logs between the students and Argumate, the students' argumentative essays, and their responses to a post-task questionnaire survey were collected and analysed. The results indicated that the students formed a learning community with Argumate in which they used various mediating tools, including online information sources, notes, translation tools, and typing assistants, to facilitate their interaction with the chatbot. Additionally, the student-Argumate collaborative writing was shaped by rules associated with meeting task requirements and following argumentative writing conventions. At the same time, the students' need for additional scaffolds beyond those offered by Argumate posed challenges to their collaboration. Our findings contribute to a better understanding of the complex interplay among students, chatbots, and other key elements in the activity system of chatbot-assisted writing and generate insights into the application of chatbots to writing pedagogy.