BackChannelChat.com was designed for teachers and includes a free version and a paid version. At $15 a year, the paid version is well worth it, with lots of important features, including a profanity filter! The teacher has full control over the chat by being able to screen comments, remove unwanted posts, private message a student, or disable a student’s posting access. In addition, transcripts can be created for individual participants or for the whole group.
Embed rich media, poll questions, videos and photos to make your chat even more interesting. Students can vote on messages to emphasize or “amplify” them and stay even more engaged in the discussion.
Here's a video overview of how it works.