In conversation, we often ask one-word questions such as ‘Why?’ or ‘Who?’. Such questions are typically easy for humans to answer, but can be hard for computers, because their resolution requires retrieving both the right semantic frames and the right arguments from context. This paper introduces the novel ellipsis resolution task of resolving such one-word questions, referred to as sluices in linguistics. We present a crowd-sourced dataset containing annotations of sluices from over 4,000 dialogues collected from conversational QA datasets, as well as a series of strong baseline architectures.