We report on a new kind of group conversation on Twitter that we call a group chat. These chats are periodic, synchronized group conversations focused on specific topics and they exist at a massive scale. The groups and the members of these groups are not explicitly known. Rather, members agree on a hashtag and a meeting time (e.g., 3pm Pacific Time every Wednesday) to discuss a subject of interest. Topics of these chats are numerous and varied. Some are serious: for example, there are support groups for post-partum depression and borderline personality disorder. Others are about a passionate interest: topics include skiing, photography, movies, wine and foodie communities. We develop a definition of a group that is inspired by how sociologists define groups and present an algorithm for discovering groups. We prove that our algorithms find all groups under certain assumptions. While these groups are of course known to the people who participate in the discussions, what we do not believe is known is the number and variety of groups. We provide some insight into the nature of these groups based on two years of tweets.