There are people with whom we would like to engage, but are unable to do so—such as celebrities and deceased relatives. Chatbots imitating these people putatively offer the next best thing; however, creating chatbots of real people can be morally problematic. This paper explores these problems, and presents six desiderata for the ethical creation of chatbots which imitate real people. Firstly, it is important to obtain consent from the subject being imitated, or in the case of recently deceased persons, their living relatives. Second, any profits generated should be fairly distributed between the creator and the person being imitated. Third, one should not exploit vulnerable persons when creating chatbots. Fourth, creators must ensure that their chatbots are as accurate as possible, to avoid reputational damage to the people being imitated. (There may be compelling reasons why some chatbots imitating controversial real people should not be created at all). Fifth, it is often morally preferable to keep chatbots—and the conversations they generate—private. Sixth, chatbots which benefit users are morally preferable to those that harm users. If these desiderata are followed, this will help ensure that when chatbots are created to imitate real people, the process and results are as ethically sound as possible.