In a growing number of contexts of use, chatbots are becoming an increasingly adopted interaction strategy. This paper explores the idea of using a chatbot in two key areas of interest: Customer service and Personal assistants. Specifically, we are interested in researching the acceptance level of this technology with regard to a user's set of behaviours, which defines the interaction process between users and chatbots. The main aim is to present a model to evaluate the most important factors that impact the acceptance of chatbots by users. To do it we devised an extension of the UTAUT model to assess the quality of the chatbot's communication in terms of completeness, clarity and transparency and to evaluate how much the user can trust a chatbot regarding privacy issues. The results demonstrate good effects on what concerns the acceptance of our chatbots by users.