There is a surge in interest in the development of open-domain chatbots, driven by the recent advancements of large language models. The “openness” of the dialogue is expected to be maximized by providing minimal information to the users about the common ground they can expect, including the presumed joint activity. However, evidence suggests that the effect is the opposite. Asking users to “just chat about anything” results in a very narrow form of dialogue, which we refer to as the “open-domain paradox”. In this position paper, we explain this paradox through the theory of common ground as the basis for human-like communication. Furthermore, we question the assumptions behind open-domain chatbots and identify paths forward for enabling common ground in human-computer dialogue.