Our chat provides a wealth of moderation tools: profanity filtering, user silencing, rate listing, and more. If you use authentication, such as Facebook, you also cut down on a ton of trolling by enforcing real-world identities. Direct moderation does require a human resource but we make it painless.
Chat message content is not stored at this time however this is something we are considering for the future. We only record that a chat message was sent by a given user with a timestamp.