I argue that social robots installed inside homes produce a novel privacy problem when they invite their users to engage with them. To build my case, I introduce relevant concepts from Erving Goffman’s theory of Dramaturgic Analysis to interpret human-robot interactions. Following Goffman, I posit that we pre-reflectively adjust our behavior to communal expectations and perform as characters when interacting with other people in public. We tend to step into character when we encounter familiar social situations, which, I argue, includes those created by robots that mimic human social behavior. Our homes, ideally, enable us to set aside the characters we play in public to pursue private tasks associated with our well-being, autonomy, and intimate relationships. As such, when domestic social robots elicit social responses from users, they may rob users of time they could otherwise dedicate to valuable private activities—an issue I categorize as a privacy problem.